I just want to say hello to you. Hello there. Nice to see you. Hi, how are you? Thank you. Congratulations. Thank you very much. Thank you. Nice to see you. Hello there. Hi, nice to see you. Hello there. Nice to see you. Mr. President. And then you open your side. Well, sir. Mr. President, you look wonderful. Well, I feel good.  Very nice to see you. Yes, very nice to see you. Well... It's the American Love Association. And we know how particular it is. And we're so happy because you're going to have more power by opening our Long Association Month of No-Number-We-Go-With-The-Officers throughout this country. And I mean, I've been moving. Well, listen, I know you have. And I think it's just great. And I think what all of you are doing, the association is doing is wonderful. And just to at least have something else for you. You got something else for me? Oh, yes, I don't have to have it. Thank you very much. Excuse me. This was seen, that's what you put on your present. Yes. This is for Mrs. Reagan because Mrs. Nancy Reagan bless her heart. She is our honorary chairman for the Anti-Marijuana Association. And that lady of yours has done some job. And she is some lady. Well, she thinks that of you and I'll be very pleased to deliver it. She sent her very best regards. Yes, she did. No, this is pearl present. That's my own present. One for you. One for her. And while I was at the Lone Association, we thought of something. And that one scarf what I thought made you might get a little chilly. So we put together eight. Oh my goodness, who put the pin in here? Oh my goodness. Let me see, I'll get it now. Can you see better than I can? Can you see better than I can? Let's see that. It won't take much time. But they pin. You know how the people that help you, they over help? Yes. Look what we put together. Eight scarves. And these eight scarves and we have made you in fact, pearls from this umbrella. For heaven's sake. For heaven's sake. And that's when our American Law Association... Yeah, let me pick up that belt. Can't put that on without a belt. It's very heavy. It can be done. Well, thank you very much. Well now, I'm almost empty handed. I just want to token of my appreciation to the Lone Association and start the contributions off. I feel I'm almost empty handed in the face of all of this. I feel I'm almost empty handed in the face of all of this. No, you're not you're not empty handed and by the grace of God you're not empty handed. I for one know it because I've known you a long time. Yes, you have. And you are the same man that always tries. I have it turns out you try. Could you have a picture? Mr. President, I want you all to join us. Yes. Mr. President, I would like to stand close to the Senate, face Senate, face Senator Long. Mr. President, I would like to stand right in the Senate, please. Mr. President, I would like to stand right in the Senate, please. And then, please. Thank you, Mr. President. Gentlemen, the President of the United States. Thank you very much. Let me first say how glad we are to see all of you here, but I imagine several others have said that already. I know what busy schedules you have.  California? Are you a dentist? But we certainly appreciate your taking these two days to come to Washington and to be briefed on the desperate situation of world hunger. All of us share a deep interest in resolving this tragic crisis that, one so staggering, it eclipses all others. We're giving it our highest priority and we'll continue to do so. Our administration has already provided an unprecedented level of emergency food aid. A tremendous amount of food has been delivered to Ethiopia and other suffering countries and much more is on the way. Just an hour ago we announced two more steps. The release of 300,000 metric tons of wheat from the U.S. Wheat Reserve and the granting of an additional 50 million dollars in food aid to be made available immediately to those African countries in greatest need. But solving this crisis is beyond the efforts of the United States government and the American people alone. Ending world hunger will require a combined of the public and private sectors in productive countries like our own. It will also require fundamental changes in those countries suffering from famine. A new path leading away from government regimentation and toward greater freedom and incentives for individual citizens to produce more. I called at the beginning of my administration for a new partnership between our private and public sectors and I have to say the result has been just amazing and confirmed what I've always believed that the people of America if you just tell them what's needed and point them at it it gets done. Well this is an emergency situation where we must put such a partnership to work immediately. I know some companies have already been deeply involved and I'm told they received awards last year for their work but I've come to make a direct appeal to all of you. We need your help. We need your time, your expertise and yes your capital investment. We need all this in helping to alleviate the short-term crisis and we need it even more in addressing the long-term problem as this is indeed a long-term dilemma. There are many areas where you can help to bring about needed change building the required infrastructure in the affected countries such as improved transportation from port to interior bringing sorely needed management skills to these developing economies enhancing their food production and food processing sectors and by your successful business practices helping to encourage the necessary long-term economic reforms in the end after all it will take a freer economy in those countries to meet these grave human problems. We face a tremendous challenge and I thank you for coming and for giving us your pledge to help all you can. When Americans stand together and work together that's when miracles begin to happen. So let's roll up our sleeves and get the job done. I know that some of the things our own people who've been there in Africa and Ethiopia maybe you've been informed that even regarding the great amounts of food that we've mentioned here these literally can only be delivered to those people who have rallied and made their way to certain dispersal centers but because of the lack of infrastructure lack of transportation and roads out there in the out country there are many millions of people for whom nothing is being done there's just no way to even find and locate them. But I recall an America that when there was an earthquake that destroyed Tokyo an America when it was Belgian relief and when it was a government that just simply said to the people here is this problem and all of those things seem to be taken over and we're done with the private sector. Well we're a little better in the governmental level now than we were then and we can do as suggested but also I think the real effort and government doesn't have resources to mention is when we suddenly call on all our fellow citizens to rally around and alleviate this suffering and this terrible tragedy that's going on and then I know that there are other things we've already in some countries had success in getting our agricultural experts and our farmers to go and help them find out how they can have something of the kind of food production that we have in our own country. Well all I can say is thank you all very much for being here for considering this and God bless you all. And if those losing those hours of sleep give you too much trouble come to my place just come to the camera and take a picture of me. We have one more person who actually works and I wish well not he's not here sir he'll miss something but sometimes there wasn't any debt time I wish well not he's not here sir he'll miss something we just wanted to show you these are the products that you're familiar with that we do of course we hope you enjoy the Friday Follies we've never pulled punches on that I have to tell you I've got to check up on someone in the distribution because I haven't been getting this one we're going to talk to your secretary I don't see this you haven't been getting the cartons no I like cartoons I start the day reading the comics alright we get about 100 newspapers every day in here we file about 45 or so of them we thought this might look like the familiar headline to you and this is sort of that was the nice one we'd like to see again in the top three and how how rude am I going to be sir if I ask you to sign that for us I understand you will certainly without recourse that's great thank you secretary I have one more thing to show you this way if we can that's a little bit of the operation we transfer that to this which is known as a grid and the White House News Summary is done especially for us and then through upstairs and through the White House operators and Walker we transfer directly to where you are and it goes to you in a matter of a matter of minutes which is quite a step up first Mr. President you know they were doing virtually hourly updates while we were on the campaign trail the little sheets we had handed that had the headlines out and that was coming through this and right into the Walker spot by the speech site you remember that it was a little puzzle how it finished the speech someplace and all of a sudden I can almost still hear him clapping and they hand me what the press is saying about the speech that primarily is it we do some other things but not very important that's a great honor for all of us to serve here I'm Des Moines Isle I worked with Des Moines Register one time when you came in there and back the first time I was there was W.H.O. and the Des Moines Register had its own radio station that's right and thanks again sir thank you very much see you see Kemp's got his uh his uh mijn uh uh uh uh uh uh me you know me man know me man All of this is a lot of 275 pounds, and they're smaller than I was supposed to be for that position. You see, I'd like to believe that there's a place in football for some smaller guys. Well, listen. You play right guard or left guard? You play right guard or left guard? Right guard. Right guard. I'm sure you know who sat around this table for so many long hours when I say, I mean, the cabinet and all the people that are in this room going at what you're going to now see. This is the recommendation that you now made as a guest to the cabinet. And today now it's in the cabinet process for them. They want to come back and suggest some changes like giving up more money. Why, please don't listen to them as we told you. We want to give them the council review also. Let me just point out, we're dedicated to this two-track policy. One of which is the deficit growth in the economy, an increase in revenues, not by way of an increase in rates, but by a growing amount, which we've had already, and we've seen that change our projections and reduce the projections of deficit because of it. And the other is that the deficit itself is a result. It's the result of too much spending. So we're trying to attack that view. If I could just throw some statistics at you and gather in myself about this thing of the part of spending plays in this and contributing to the deficit and that the increased spending over the years has been counterproductive, not only economically, but counterproductive with regard to what it was supposed to do. For 1950, I'm up into the 60s, the rate, there was a decrease in the percentage of people living below the poverty line. And then in the late 60s, Johnson's war on poverty, the great society, was passed and replaced, and actually it started reversing the decline in the percentage of people living below poverty. That began increasing, and under the previous administration that was increasing at a rate of about 9%, we have cut that almost in half since 1981, that rate has increased, but still increasing. Now, from 1965 to 1980, the budget increased to about four and a half times what it was in those 15 years. But the deficit increased 38 times what it had been in 1965. So again, I say that we say the bill is spending. And I think that this is an emergency time and it's a moment in history, and if not us, who, and if not now, when? Corral is to get it back. So this, and we also are pledged to do the simplification program of taxing, but we don't want to get into there with our opponents. We don't want to get into a trade-off type of thing with them and their tax increase ideas. So both of these are top priority. We want to go with this first, the budget matter first. And we've taken one of your suggestions with the idea of encompassing it in a framework of various reasons that you will hear when Dave gives you the report. He, but I'll save some other things for the discussion that we'll have and then have after Dave is finished. I was going to be asked, the first part of the meeting, having been through all of this, but I overcome my, or overcame my dissertation hearing grown men cry. Nice to see you. I know we're a little late getting across the street. We've been whittlin' at the budget in here, and it was like playing overtime. Well, listen, I'm pleased to do it, and I'm forwarded. We have just a little souvenir for you this year. Thank you very much. Yeah, George Bush. Is Father Monon with you? Yes, he is. Well, I'm kind of excited to say this. Well, shall we all go across the street? We're supposed to go. Our daughter went to BC, Dartmouth. I want to see Father Monon. It's a great thought. How are you? This, I'll give this to your mommy and daddy. This is a jelly piece. We will bring this to the family. Nice to see you. Nancy? This is cool, right? Thank you. President, I'm sure you're the Marchandana. Well, now I'm going to sit down and sign this proclamation, which makes January the month of birth of that prevention. And I think we have a wonderful of what is happening here. How much we owe the March of Dimes for all that they've accomplished and made things like this. There. And I also hear that you hate me. I understand they want us to come over in front of the fireplace for a picture now. You got a surprise? Wow. And everybody else is here. Not me, yes. I have a feeling that if I say ranch, I'm going to have some problems here. We'll work that out. Whichever place, maybe we're going to have to get it a sheep. I thought she was just showing us her dog. I was surprised, and Preston. Yes, you were there. Christian, what's the name of your dog? What do you think the name should be? Christian, you know something? We once had the most wonderful dog, I think, and she was just named Lady. And maybe what we ought to start with is maybe we should name this one Lady Two. Is it a female? Yes. I'm sorry, I've run out of time to name something else. Thank you, Mr. Warren. Christian, thank you very much. Love around you. Success to the driver's always. Thank you. I'm sorry to get to see you again. I can see you. It's all your Sunday night. I know. Kathy, keep a copy of the magazine. Down in the air. It's fairly able, we found the Douglas. Congratulations. Thank you. Say important words to Ditas. Pleasure. Thank you very much. Thank you. Joe McKinnell, would you like to say a few words? I see you. Jim Gull, Marlon de Ruex. Nice to meet you. Nice to meet you, sir. Marlon de Ruex. Mr. President. Bill Baker. привance to see you. Virginia Morris. Ken Gotcha. You just got a notice to meet you. We'll say no hemen. Well, I want to thank all of you very much for all that what you're doing with the program. You are the first of all in our education. I hope we'll be finding the lines of science and mathematics and all of that by this program. And I heard also of something called Astronet. Maybe I could give you a message if you were to put on an event. Do have that. It's been a long time since we sat over there and just got to this. Yes. Now we're, now we're launched. We're on our way. We're looking good. We've got six hours of school to go. If you're thinking about me, I'm here to brag. Thank you very much. Do you want a group photo? If you want it, can you? Sure. Is it too wide? Thank you very much. Thank you. Good morning, Mr. President. Good morning. How are you? Good morning. Thank you very much for your congratulatory letter. I'm not going to listen to who say thank you, but I am very grateful. I am glad to be able to say in person congratulations. Thank you. How are you? Very nice to see you. We have a good friend in back out. Yes. How are you? I'm sure. Hi. How are you? Welcome. Thank you. I want to say it properly. At least here. Well, why don't you come in? You sit over there. Hi. Good eyes on you. Nice to see you. Thank you. Jack? Yes. Yes. Presenting Bishop of the Episcopalian Church.  I see. So you can tell the bishop no matter what we say, that I behave well. Yes, I think I'll give you good. Very good. Yes. He's a lovely man. He is. If anyone warned Bishop Tutu, they may start yelling questions, which I think you'll have a chance to answer later. But this is supposed to be focused, but the press, they like to call out questions. So you may have to say it. Yes, I was told. Until afterwards. That's well done. Bishop has called your policy in South Africa evil, immoral, and totally un-Christian. What do you, what do you even say to him to change his mind? That's the answer. Will we be able to talk to you later, sir? Much later. Do you think you can change his mind? We believe when people talk to each other about each other. We believe that Iran is collaborating with those hijackers. I'll be taking it. The boys are going to get you. Yeah. I'm afraid you may be right, yeah. That's the one. That's the, that's the, that's the scant.


But this is part of the course of Donald Trump. This is who he is. This is what he is. I think much more concerning than actual Fourth of July parade has been Donald Trump's cozy relationship with the murderous dictator, who I never call by name, by the way, because I don't think he deserves that kind of respect, the murderous dictator of North Korea, the floundering kind of non-strategy in Iran. The actual policies and actual presentation of the presidency by Donald Trump is what really scares me and upsets me. There was this beautiful video of this North Korean dissident, this girl who managed to escape North Korea at a massive cost to herself and to her family.  She said, what message is Donald Trump sending the North Korean people who are being enslaved, who are being tortured, who are being raped, pillaged, murdered by this regime? What message of hope is he sending them? He's basically telling them, oh, no, your ruler is just like any other ruler.  I'm going to treat him with respect. I'm not going to fight for you. I'm not going to even morally fight for you. I'm not advocating for the United States fighting for the people of North Korea. But morally, what does this mean? When America sanctions the kind of evil that Donald Trump is being sanctioning in his relationship with the North Korean brutal, murderous dictator, shaking hands with him, hugging him, calling him as he's got a love thing going on. And then walking into North Korea as if it's any other country, as if it's just another border, it's just another regime. The message he sends to North Koreans, the message he sends any oppressed people in the world is that America is nothing that America is meaningless. And America will not stand with them. That America is no longer that beacon, not fighting for their freedom, but a beacon, for freedom, that that is long past, that has gone, and America does not actually stand for their freedom. That is, that is a real travesty and a real, and it's not that other presidents have been significantly better about this, but Donald Trump has taken it to the next level. Donald Trump is in this sense more deflating of America's value. I mean, everybody criticized Obama for America not leading and they criticized Obama for kind of moral equivalence between America and other nations. They criticized Obama for bowing to the Saudi prince. You know, everybody went after Obama for not being a real leader, a real defender of American principle as well.  This is the lowest, I think, American foreign policy has sunk in terms of abandoning the idea of the value of liberty and the value of freedom to people around the world. And, you know, it's hard for me to understand the people who are defending this and there are plenty of them and there are plenty of people who listen to the show that have been defending, oh, this is the best alternative because this beats going to war. Why is war an alternative to this? Was not an alternative to this. You can shun this brutal dictator and still not go to war with him. Indeed, North Korea doesn't want war.  He doesn't want to die.  And to treat him like anything else is a great travesty. Many people say, you know, this is just like Nixon going to China in many respects it is. Just like Nixon going to China and Nixon going to China was a true travesty. I'm actually right now trying to find this quote from Mayan Rand where she wrote about, you know, Nixon going to China and what that represented and what that meant. And, you know, and she thought it was an abomination. And she wrote very eloquently, that's why I'm trying to find it because I think it was so, it was a powerful statement of the United States basically abandoning the principles, the banning the principles of which it stands, abandoning what it represents in the world and what this meant for people in countries that are striving towards freedom and what this meant when the United States abandoned them. You know, is completely gone. So anyway, I can't find it. So if I find it in a little while, I'll read you that quote. So, you know, I think this is a particular sad time for America. It's a particularly sad time for America. It's a particularly sad time to be celebrating the Fourth of July with a president who has no, I mean, no understanding of what this country really stands for. And we'll get to that in a minute, but here is the quote from Wang Yuan. This is what she wrote about Nixon in China. Quote, morally, it was impossible to watch all those gracious ceremonies, benevolent smiles, lengthy handshakes, cordial speeches and hold in mind the actual nature of red China when kept alternating between two feelings. The kind of unreality and childish amusement one feels at a circus and the shock of returning to reality. The reality of China's terror, starvation, torture chambers, mass slaughter. I kept thinking of the thousands of men who tried to escape from China by swimming many miles under the gunfire patrol boats to reach freedom in Hong Kong. What about them? I kept thinking. Whenever somebody uttered one of those ringing speeches about universal peace and love for mankind, isn't there anyone to defend them? The shock came from the realization that the smiling figure in the midst of the ghastly pretense on the TV screen was the president of the United States. It is America that all the enslaved peoples of the world look up to as the symbol of freedom and as their last hope for the Chinese to see an American president drinking toasts to their jailers is so cruel a blow that in the name of humanity, no one should ever permit himself to deliver it. Now, that's how I ran at a finest. That's how I ran at your beautiful articulation. I could have never said it any better, but that is, there is no different between that and what we are witnessing right now in the case of North Korea. Now, some have said, but Nixon led to the opening up of China and to all these Chinese being freer today. Well, no, he did not. His trip was never necessary for that. China was not opened up, China was not freed up until Mao Tse-tung was dead deep in a grave. And only then China was freed up somewhat. And that freedom was not a result of America opening up. It was a result of the pragmatism, the brutal unwavering, brutal pragmatism of Deng Cha-peng. Deng Cha-peng was a bad man, but when it came to freeing up his country in the name of pragmatic economic reform, he did it because he saw it worked. He's also the man responsible for the slaughter in Tiananmen Square. So he's no hero of freedom. So no, Nixon's gesture did not bring freedom to the Chinese people. Nixon's gesture did not create economic progress. Nixon's gesture was just a sheer unequivocal, unmedical-ended betrayal, betrayal of those in countries like China and North Korea who still strive for freedom, who still look up, who still dream of escaping as was articulated by that brave young girl who criticized President Trump for his meeting.  It's an authoritarian regime. It is far closer to fascism than communism, but it is neither fascist nor communist. It is a different type of authoritarianism. Nothing has to necessarily fit into neat little boxes like left and right, this tribe or that tribe. There are new forms of authoritarianism. And China has created one. It keeps the Chinese Communist Party label because it is a convenient label and because it would like to rewrite history and present Mao Tse-tung as a hero and the Communist Party is good. But there was no communism in China. There are no communists in China. There is a market, to a large extent, a market economy, at least in vast segments of the Chinese economy, are relatively unregulated, relatively free, relatively low taxed. The welfare state in China is actually smaller than the welfare state in the United States, smaller than the welfare state in Europe. So no, trading with China is not like sanctioning a regime, a brutal regime, where there is a single dictator who rules over everything, where there is no economic freedom, no political freedom, no freedom to travel, no freedom to enter, no freedom to leave, where you're shot at the border. That is the border, by the way, that Donald Trump crossed. A border that if any North Korean was going in the other direction, they would be shot. That is not a border one recognizes. That is not border one crosses in a friendly gesture. It is hard, and I don't know what to do to convey to you the extent of the evil that that represents. I read the quote from Mainland.  And the fact that so many people, so many people who have called themselves pro-American, who still call themselves pro-American, support the president in this action. I see it on Facebook. Is truly, truly scary, ominous for our future and ominous in terms of the understanding that Americans today have of what it means to be an American and what America actually represents. What we need today, what I call the new intellectual would be any man or woman who is willing to think. Meaning any man or woman who knows that man's life must be guided by reason, by the intellect, not by feelings, wishes, whims, or mystic revelations. Any man or woman who values his life and who does not want to give in to today's cult of the stare, cynicism, and impotence and does not intend to give up the world to the dark ages and to the role of the collectivist broods.


Good morning guys, it is actually like 6am, I woke up naturally at 5.45 which is only because I got back from Georgia last night and I'm on East Coast time. Which is fine by me because I'm trying to start waking up early and I think that this is the week that I'm going to be able to do it. Just made some coffee, I'm in my room, I don't have class until 9 so I'm going to do some readings and just have a nice morning to myself. I'm very excited about this but if you guys are new here be sure to subscribe. This is going to be a really good vlog, I have some really fun stuff this week so I'm really excited. Bye. Good morning guys. It is now like 7.20, this is also the hairstyle I've been wearing every day of the past three days. I'll take a little kindergartner. My leopard scrunchie that I got in Georgia, watch my Georgia vlog if you guys haven't already. I'm just putting on some earrings.  Today is going to be super fun. I'm back in class, well I didn't miss class actually I don't know what I'm saying though. But I'm in class, I have to stop by the studio on my break. Yeah it'll be really good, I'm excited, I love going to the studio. Woo that hurt. I've also been listening to TK's Juicy Pod with Alicia. So good. Guys go check it out. Okay so I have my jewelry, I'm probably going to, I'm just wearing sweats and a big t-shirt. I'm probably going to grab my red jacket, yeah this is a no for me. Am I really going to wear this jacket again? Yeah. Alright I'm ready to go walk Coco. It's the Georgia weather. Hey guys on a break, what's up, we're on our way, I have to stop by the studio really quick on our lunch break to record some interest in the podcast and then come right back. So that's what we're doing. We're valing the studio, every single thing that has, we're in a time crunch and everything's back that could happen but it's fine. Got the valet ticket, we're good. We made it to the studio, wow I just found a tripod, can you believe that, yeah what should I say about Ryan's intro? Ryan is the king of Leon, the original king of Leon. Did you see his Instagram story last night? Oh my god. That was his best thing he's ever posted, I couldn't believe it. No I seriously. I'd like to address what was leaked to me in my house.  Dude I was literally king so hard, as far as me in my house. Alright Kenzie whenever you're ready to go. Perfect. Hey guys what's up, wait that's not what I say in my intro, never mind, okay. Hey guys welcome back to the I Love You So Much podcast with me, Kenzie Elizabeth. In today's episode I am so excited for it.  Good afternoon everyone, I'm in my kitchen, I'm making some food, I'm cleaning, doing the dishes, just all the really fun stuff. I have Delaney free, I'm really doing y'all, I have Delaney free, it's jazz playlist playing in the background. So I have like about an hour and a half until my cousin's gonna get here and we're gonna go boxing, grocery shopping stuff, just made some food, I'm gonna get some work done pretty much as much as I can. I literally wasn't talking to you girly. Um, I said some water, I'm trying to drink a lot more water and I'm just gonna get some stuff done. This is actually like my favorite time of the day when I come home, get my office feeling good, candles lit, Frank Sinatra playing, drink some water, food, get some work done. Love this time of the day, it's the best. Hey guys, another car shot, I know you're probably shocked. I have the biggest headache, I'm so exhausted, so I'm going to go work out right now. I'm gonna try out a new boxing gym, hopefully I like it, I'll let you guys know, I need to take my earrings, my jewelry up, it's called Nine Rounds and what I like about it is that there's intervals starting every three minutes so you can just like hop into a workout, which sounds amazing. So I'm gonna head over, also chopper stone merch, link down below, check it out, new hoodies are coming soon. Okay, it's my first time going to this place so I'm not gonna vlog inside, I'll see you guys after, I'm probably gonna be dead after, which is awesome, I could sleep right now for the remainder of the week, so good. Ah, back for my workout, it was like they just had me do the beginner's workout so it wasn't like horrible but it was fun, I need to get gas, I'm glad I worked out but oh my god I'm dead, okay, well awesome.  I just woke up and made some coffee, I have the drunk elephant baby facial on my face, I noticed I had like weird texture, I think maybe from traveling, so I just wanted to do that so we just get it all off but I'm about to do a nice little divo, a morning reading if you guys are interested in those, I have an entire video on them, eat some breakfast, today is Wednesday, I have class at like 10 30, we have her night tonight which is like a really really big thing at Zoa, it's really cool if you guys are a girl and you live in LA, definitely come, I know that you guys have seen this later but it's awesome, so I'm super excited for that, you like get a little more dressed up, whatever, I need to draw my car if you get a service, just like stuff like that, you know, drinking my coffee, I love Wednesdays, I honestly love days when I have class more than when I don't have class, I just love my school, I go to ZLC by the way, I don't know if I said that in this vlog, Zoa Leadership College, it'll be like, all this will be like down below if you guys are interested, check it out, okay guys it's like 8 something, I just got ready, I'm just wearing really comfy clothes because we're gonna change into like nice clothes after school and there's something on, the AC is so loud in here, I'm gonna go take Coco on a walk and then I'm gonna drop my car off to get service and then Christina's gonna pick me up and then we're gonna go to class, I feel so weird without like chapstick on or anything, that's my thing, like if I don't have chapstick on I'm like, that's it, like some people are like makeup, full face, no, I'm just chapstick, that's all I need, listening to the new gals in the go podcast, their new like graphic is so cute, awesome at this moment, I've been up for hours and just now have my lip balm to put on guys, whoa, so I'm gonna head off to Firestone, drop my car off, which is just fun stuff everyone, I feel like I'm always taking my car and everything but it's like things that I'm supposed to put, it's never anything crazy, so okay you know what I was just thinking, my Firestone segments in a vlog should just be like a segment, like it should be a thing, but I guess here's the thing, I've told the story before, but I'm like a hypochondriac with my car, since my tire blew out on the freeway with Danielle, Molly, and Brooke we were talking about this this past weekend in Georgia, anyways, so now I go to Firestone, now I know why I go to Firestone all the time, because I always think there's something wrong with my car when there isn't something wrong with my car, but I have a service, like it does say this car needs to be serviced and like I don't think that they can tell me that it can't, but yeah I'm like friends with people at Firestone, I walk in and I'm like hey what's up, they know me, I know we're on a first name basis, the coffee there's really good, I always get hazelnut, it's so bad, I'm gonna walk in this morning and they're gonna be like hey Kenzie, what's up, what's wrong this time, so yeah I don't know why I was acting like I don't know, I think I just like forgot, I had like a really lapse, like lapse of my memory, but anyways today my car actually doesn't need to get serviced, so they can't do anything, I'm gonna be like guys, today is the day, today is the day, all right everyone it's Firestone time, favorite part of Firestone when I make the coffee, it looks like really gloomy, I feel like I'm not, I don't know, oh, is that good, and then Christina's car, Christina the angel picked me up, taken me to class, I dropped my car off, I walk in and they literally go hey Kenzie, what's wrong now, or what'd you do, and I was like oh my gosh, hey Dan, how are you, how's the kids, he's like where's your dad, because he always talks to my dad on the phone, and because I'm always in class, so my dad please help me, I don't know what I'm doing, even though I do, my dad doesn't Kenzie is queen of making friends with car salesmen, she got me $30 off, $30 off, always befriend your car people, mine think I'm crazy, but Christina had to get her battery changed, so last week I went in, befriended Hector, it's so easy, like go to places where like you're going often, also be nice to everyone anyways, but like things like that, especially when you're a girl, go in, befriend them, and then tell them what happened on Saturday, on Saturday, I go back, two days later, I pull up the fire stone, there's 17 cars in front of me in line, I'm like I'm so sorry Hector, I don't have time, I'll come back, and he says hey, don't worry about it, I'll take care of you, before everyone, right now, because Kenzie befriended him, yeah because I mean yeah we had to listen to him, he preached for like an hour, we really befriended him, but seriously I do that everywhere, and like I don't pay for coffee normally, I like literally like I have so many life perks, because I'm just nice to people, and I talk to them, and I ask them about themselves, all you have to do is just ask people about themselves, they love talking about themselves, walking to class now, my everyday clip, um oh I need to put this away, why are there always so many light leaves, we have a teaching, and then lunch, then track, then her night, very excited, my office just doing some work, I picked up a new role of film, so I have a ton of disposables from this weekend, heated up some food that I made last night guys, I am a chef, this is incredible, playing the jazz playlist, just gonna do just like an hour or two of homework before we head out, this is bad, but I just really need another coffee, I'm so, okay, the office has such a great vibe, I love it, I just got a lot of homework done actually, pretty much all of it, besides no I didn't get all of it done, I'm in work and I planned, I'm gonna go get ready quickly, basically we're gonna be there for a while and I don't have to get actually ready until later, so I see to pack a bag, my hair looks amazing, so okay I packed my bag, I'm back in my really comfy clothes, I have another outfit that I'm gonna change into later, probably not gonna vlog too much tonight just because I can't really, but tomorrow it's gonna be really fun day, um so we'll see what I get, just warning you guys, because it's not like, not like a vlogging time you know, okay guys so it is like midnight, have a big glass of water, just showered back from her night, it was incredible, I left my vlog camera here, but I mean I really wouldn't vlog there anyways, but it was so much fun if you guys are ever in LA and when there's her night or you live here, hot, so anyways, tomorrow morning I have like demo groups and then actually Alisha and Remy's podcast launched today, which is super exciting, so I have their launch party tomorrow and then yeah just think a bunch of stuff, Ryan's podcast, like I'm so excited, the podcast with me goes live in the morning, we were just talking about it like an hour ago, we're very excited, so I'm just super pumped, yay, life is good guys, Thursday morning, so it's my last day of classes for the, oh that was rude, it's my last day of classes for the week, we actually, we normally go in, we have like demo groups and then we go in, we have like chapel at 1030 or something, I thought yeah, I know my school schedule I promise, we go in at nine essentially on Thursdays, but they gave us off until one and we're just working on our outreach groups, so I only have like two hours of school today, but I was already up because I wake up early now guys, so I just got a lot of stuff done at home but it's 1030 and I'm like there's really like not that much that I can do without like a few meetings that I have to take tomorrow, oh my gosh guys, so exciting, my podcast with Ryan is up now as of today, you guys haven't listened to it, it is my favorite episode ever, Ryan is literally the best person ever, you guys have definitely seen him in the vlogs, he's like everyone's most requested person, but I'm just so excited about that, so yeah anyways, I'm on my way to Starbucks, I think I'm gonna just do a little bit of reading there, I'm really just like super motivated right now to learn, which is really good because I feel like I'll get, I feel like I normally for the most part am, but I don't know if I necessarily was like focused on that recently, I think I was distracted, but now I'm like super excited, I'm awesome, why am I on the topic, I have two things for you guys, well one thing, listen to Voo Church's Trapped in Offense, it's in the Love Lies series, you can listen to it on the podcast, I'm sure they have it on their YouTube channel too I think, but listen to the Trapped in Offense podcast, it is so freaking good, I listened to this a few weeks ago, but I was considering listening to it again this morning just because it's like that good, like it is like, that is like a message that I will always think of for the rest of my life, it is amazing, so check it out, anyways I'm gonna go to school, I'm wearing a Backstreet Boys t-shirt, um yeah, so it's gonna be a good morning, I'm meeting with my group at Starbucks that noon, but I'm just gonna go right now, I'm gonna be there like 1030 and just like do my own thing for a little bit, yeah, I just, I love my life right now, I do this all the time, I feel like I'm vlogs, but I just love my life, I literally almost teared up on the drive here because I'm just ridiculous, I think I'm gonna cry, anyways, I'm really excited because I'm really craving Starbucks, you know when you're really craving Starbucks and you're just half an hour or so, be on your way, which is like all the time, but it's like the only place to go to, I am, oh, what, what is wrong with me, I'm so sore, my calves, oh my gosh, like, my car's not even unlocked, I can't explain the pain much later, I do not remember the last thing I vlogged, I went to class today and then I went to get like lunch with a friend and now I'm picking Taylor up, I don't know where she is, we have Alicia and Remy's launch party, which I'm sure it's gonna be like so freaking cute and perfect, they have their podcast out, which I already mentioned, pretty basic, which is so cool, listen to it, and they're literally number one on podcasts, like that's huge, like the people, the number, like the top spots on podcasts, like don't move, so that's really crazy, I literally changed the veggie girl parking lot, I'm wearing like a dress and a parking lot, I would do that though, but bathroom, I almost said grocery store, today is just not my day, but yeah, that's it, I got ready in 0.2 seconds and we're gonna, yeah, I have been listening to her, look at Taylor, go, I can see, I'm sure this one looks good, I want to say Merry Christmas and happy holidays to everyone, look at me, see, about decorating Christmas next week, good before they're even editing, I wish we would have just, I love that one, I love that one, it is currently 8am, I just got off the call, I have a lot of calls today, I'm filming a ton, I'm recording, I wasn't going to go to town because Ryan and Taylor are recording podcasts, but that got me until tomorrow, so now I have a bit more time to get everything done, so I'm already like ready, I mean I didn't show my makeup because I'm gonna film that, but I'm gonna head off to my office, oh that's Taylor, and get to work, okay, hey guys, okay, I don't know why, it's actually like I was starting a new thing, okay, I just filmed two videos, it's 10am, I've been listening to the Gary Vee podcast with Scooter Braun, it is so good, so anyways, I don't have studio time until like three, and I swear on a few errands before, but I'm gonna try to get as much editing as I possibly can done, just see what I can knock out, maybe I honestly I can probably get, yeah, I'm gonna get these videos done basically, that is what I'm gonna be working on the next few hours, just some editing stuff, and then some studio stuff, currently editing, I just made some lunch, I made a sweet potato, and then I just made some vegetables, what a health queen, but yeah, just getting some work done. Okay, this vlog is getting really long, so today I'm actually, after this, gonna start a weekend of my life vlog, and vlog for the weekend, which this weekend is gonna be super fun, I'm really excited, I've got a lot of work done, and I'm just gonna keep getting work done, but I hope you guys enjoyed this week in my life vlog, I feel like I like my one before this one better, there's more people in it, but yeah, I was just kind of like getting my life back after traveling and like, you know, college stuff, but hope you guys enjoyed, I love you guys so much, and I will see you guys soon, bye!


What's up everyone welcome to tutor terrific. I am so glad to be here in my first live stream I don't know who's gonna show up. I had issues. I use StreamYard as you can tell. Oh gotta get used to that right up there if this goes well, I'm going to definitely look at Purchasing something from them. This is their free version right now like test it out, but Welcome everybody. I had some issues Posting these live streams on the channel so that you can see them. It wasn't showing up in the videos feed I don't know why when I scheduled this thing, but I made subsections under that So that you can see Upcoming and past live streams and when I'm live too, so those will show up soon But hey, this is my first time doing this and I am super stoked That YouTube makes this possible. I'm sure you've heard that before but I'm new to the game But I want to help people. I want to help people all over the world. I want to help people No matter where they are with what they need help with when it comes to Educational endeavors so let me know either in the Chat over there or in using that email address as I put in the chat. Let me know What you need help with whether it's something content related or a specific problem. You're just having trouble with a concept I'm here to help and I have something planned just in case No one is a game right now and that's just fine. I've got a lesson on partial fraction decomposition Which people seem to be Think is quite hard and that's just fine. So We're gonna do that until people show up And we'll see people show up. It'd be awesome if they did but Yeah, if I get a lot of people when I get a lot of people I will Certainly any donations any Things you do like super chat or the little thanks heart are awesome. I will definitely be Prioritizing the super chats that come in and the questions that people have if they use super chats So we'll see lots of things to test out here, including stream yard itself very very stoked for this whole thing So without further ado, let me get my screen shared here and let's look at What I'm doing on This particular Thing here called my screen Just Let me figure out got to share that screen You know how to show my screen. I thought this was it. Yes There it is We're gonna share this one over here All right, so you guys should be seeing that now Partial fraction decomposition by the way, I have discovered a long time ago one of my students showed me this thing called Miro and Yes, of course we've had zoom for you know, two three years now and It's been really annoying and their whiteboards aren't very great But my friends showed me this thing called Miro and it blows Zooms whiteboards even their new whiteboard feature out of the water This is a game changer and it's free and you can share you or basically your whiteboard universe space Which I will show you here. I have this lesson planned for partial fraction decomposition, but I'm not even Like I can go anywhere I want and I can add graphics I can add graphs I can add images I can add YouTube videos I can actually embed videos into this This like universe whiteboard space and multiple people can be Live going on here and working on it, which is great At the same time and you can like if you have multiple people in here You can have someone up at the top here You'll see all their icons and you can click on their icon and go right to where they are if you're lost and follow them around while they're writing it's really cool and it doesn't seem to Limit who how many people you share your board with they call it? This is my board called YouTube lives But I have another board that fits every single one of my two drink students every single one They get their own little section of the board and they just know to go right to it when they start my private students sessions so Yeah, let's do this partial fraction decomposition. Okay, partial fraction decomposition is You could consider when you're getting new to this topic the opposite of Combining fractions with unlike denominators or like denominators, but combining fractions with Rational expressions in them. So not just numerical fractions, which are easier but algebraic Expressions in the numerator and or denominator like we have here so This understanding this guy's is going to require you to have some algebra background Certainly if you're not using common core style math, you should be through algebra one for sure definitely But having algebra two under your belt is a plus being in pre-calculus is where you would learn something like this Maybe some of your schools call that trigonometry if you aren't in If you're in a common core setting, I would want you to be in math three before you start to learn this but hey If you think you can follow along and you've combined fractions before you probably keep up But let me tell you It's the opposite of what I'm about to do, but I want to give you an example just to get you in the zone here So if we have two over five plus x plus six y over six minus x we have different denominators And so we have to combine them the proper way. We have to combine them Using Least common denominator we can use a other common denominator, but the least common denominator will assure us that we don't have to do any Simplification later. So now we need to find the LCD. Okay, that's the first step so when you have Rational expressions in your denominator like this the least common denominator will have one copy of Every unique factor and one copy of every common factor Again, let me say that one copy of everything unique one copy of everything common Okay, so there's lots of different ways that teachers teach that but this is how I do it Let's look at the denominators here We've got five plus x and six minus x you might say well They both have an x but x is not a factor Five plus x is a factor and six minus x is a factor and that's all I care about are the factors So these are unique. They are not identical. And so the least common denominator will have one copy of each in its Product, okay, these common denominators a product of factors Okay, so this right here is the least common denominator, okay, and you can choose to multiply that through With the double rainbow method or the box method whichever like you like better you would get 30 Minus 5x plus 6x which is just x Minus x squared and I'm a stickler for writing things in standard form. So you'd have you'd switch the order here and put the negative x squared first the next lowest power of x in the middle and then the constant term at the end plus 30 and Then you'd have your least common denominator all multiplied out or you can just leave it factored like we have up here It's up to you. I like it. It looks a little cleaner like this So I'm that's my preference. So what we're doing is we are going to multiply each of these fractions by what their denominators were missing from the LCD, okay? That's what we're gonna do right now. So This first one 2 over 5 plus x it was missing the 6 minus x From the LCD it didn't have it downstairs. So I need to multiply using the denominator numerator same quantity rule Okay, let's find what that is. I can multiply a fraction by Any non-zero quantity as long as I multiply the numerator and denominator by the same non-zero quantity. I Will get a fraction that has the same value. That's really helpful because I Can change what the fraction looks like even without changing its value doing it this way Zero doesn't count. You cannot do this with zero at all at all at all when you multiply by zero over zero first you're multiplying by something that's indeterminate doesn't have a determined value and You're getting rid of a lot of information when you multiply something by zero because the product is zero and there's nothing left So we don't want to do that What we do want to do This we want to multiply by the factor again From the LCD that was not present or all of them that were not present in your Fractions denominator in that case it would just be six minus x so two over five plus x turns into this Now the we'll do the multiplication in a minute, but next what we have to do is we have to Look at the next fraction six y over six minus x and say hmm. What's missing from here? Well, I'll show you Six y over six minus x. I care about the denominator guys six minus x downstairs That's missing from the LCD the five plus x And so I need to multiply the top and bottom by five plus x Okay Don't start cancelling stuff if I cancel like this and like this because I have my Cancel trigger my cancel finger on the trigger that's not gonna be good. So don't do that. Okay, you need to put You need to multiply okay, don't put anything you need to multiply so on top we're going to distribute the two in the first fraction That's 12 minus 2x and Then other fraction that'll be six y times five that's 30 y Plus six y x or six x y if you like doing things in alphabetical order like me and I'm going to use that nice Multiplied out version of the denominator negative x squared Plus x plus 30. It's not just any denominator. It's the least common And so here we have now Two fractions that have the same denominator, which means we can add them How do we add fractions with the same denominator? Well, we make really one fraction with that like denominator Equal denominator. I should say so one copy of that Negative x squared plus x plus 30 for one fraction now Just one fraction on top We're gonna add these two expressions now. We add using the rules of like terms Terms that are like Can be added. What do they have to have they have to have the same variables to the same exponents? If they don't you can't add them Any more than you could just write them next to each other with a plus or minus sign between them So let's look here 12 minus 2x 30 y 6 x y None of these are like that's okay. It doesn't mean anything's wrong. It just means you have to write them With a plus or minus sign between all of them You just end up with this Right here Fortunately, that's really weird complicated But most of the reason why is because I had a variable up top in the beginning So that's combining fractions with unlike denominators. Okay? We're gonna do the opposite of that. We're gonna start with something. Thankfully not something this crazy over here But we're gonna start with the end and go back to the beginning Okay Step one when we do this. Okay, there's a specific step order when you have your fraction If it is improper you must divide so you must divide if Improper, okay, you must divide if improper So if you have a fraction with a higher degree By the way, I'm rolling into do examples that have one type of variable in them Like x or y and it's the only one but If it's improper meaning the upper degree is higher in the numerator than the lower degree That means the higher power of x is on top Then you have to use long division or if you can based on the format synthetic division To get a quotient and a remainder and that remainder as you know from long division You're gonna write that remainder over the divisor over the denominator That will be proper and then you can move on. Okay So if it is improper Right remainder, I'll just call it r of x because it's a polynomial itself right r of x over The divisor I will call d of x and continue To step two, okay Now step two. What is step two? Step two is to set up Your denominator properly you need to factor the denominator fully fully factor Denominator you need to look at what your simplest factors look like. All right, you know, I'm a demon Denom for a denominator for short. Okay? You want Factors that look like this. Okay? one of these two types Linear factors Those we're gonna say have the form px plus q So x is our variable P and q are numerals coefficients and It can be raised to any power Obviously the more complex it is the more the higher the power of m is or they could be quadratic a Little bit more involved if they're quadratic, but those could look like this ax squared plus bx Plus c notice how x is squared in these and that could be raised to any power We'll just say different one than the other one to the end now these are Irreducible these quadratic ones. I'll explain what that word means irreducible when something's irreducible over the reals Or over The real number set are that means I can't factor it. Okay into nice rational numbers Okay, or even irrational numbers This thing has complex solutions if it has any so that's what we want We want an inner reducible over the reals. No factoring possible. That's the main point Okay, if it if you do have a quadratic factor that you can factor further do it and turn it into a linear factor, okay now Step three is really depending on what type of factors you have for linear factors of that form px plus q to the m We have to set up Partial fractions. Okay on top the numerator will have just a number Each numerator will have a unique number Well, they could be the same. We're just going to pretend like they're not give them each a different subscript and a 1 a 2 a all the way through up to the power itself and That the linear factor is raised to on bottom We will have the original linear factor But each time we write it We write it to one higher power Wow pq plus q come on. Hello px plus q Now it'll be written to the squared power It's the second term we go all the way ppx plus qq px puts p to the fourth all the way up to whatever m is px plus q To the m. Okay, sometimes you're really gosh. All these are this long. No, they're not They're not all this long. Do not worry. Okay next For the quadratic factors the setups a little different on top will actually be linear B1 x plus c1 For the first one and on bottom you'll have that quadratic factor Raised only to the first power remember. This is irreducible Okay, the next one will be a whole another set of coefficients with that x be a b2x plus c2 Just the little two subscripts mean it's different than the other ones in the previous fraction and that will be raised That'll be divided by a denominator that is raised to the second power So we're going to continue doing this All the way up until we have m fractions matching the power. Oops. I'm so sorry. That should be an n It could be different than the other ones. We're going to go all the way to n whatever it is be nx plus cn all over A x squared plus bx plus c to the can you guess it? and Okay, again looks super complicated, but What we're going to do next Will hopefully make sense of this okay getting these coefficients on top or these numerals on top is the work that you must do And so we need to do that So here's our first example Okay x plus seven over x squared minus x plus six now When we do this We have to start by making sure we have a proper fraction and it comes to degree and We do here the top degree is Smaller than the bottom degree. How do I know degree? It's the largest power of x in the polynomial that you see So the numerator polynomial It's x to the first power the denominator polynomial The degree is to the highest power of x is to so the bottom the denominator has a higher degree So it is a proper fraction. So we're going to skip right to factoring the denominator Okay, look here. This is a trinomial a quadratic one and so we look and see that the first coefficient is one So we've got a simple method for factoring this what two numbers multiply to negative six the constant term and Also add to negative one the coefficient of the middle term and the answer I'll give you a second to think about it Six is one times six or two times three Negative six we've got to have one of those be negative Combination that works such that they also add to negative one would be negative three and positive two like that And so what we do thankfully get to skip all of the intermediary group factoring steps From the AC method. We just skip all that we get to write Two parentheses already multiplied together each start with the x and Then you add in these found numbers From your little exercise over there Okay, hopefully you've all seen this before if you're not familiar with that you're gonna kind of be lost Okay, so maybe you're not done with algebra one or you aren't done with math one yet ouch. You've got to know your factoring Okay, that's okay. I shouldn't say ouch as you just say This is a little bit beyond what you're able to understand most likely But that's factoring and I fully factored the denominator. I have beautiful Factors that are linear, okay Now but they're they they they're each raised to the first power. Okay, so I must have One Partial fraction for each one of these, okay The first one will just be a on top over x minus three It wasn't raised to a higher power So I don't have to add more fractions and more letters more versions of a on top. I'm done with that one But I've got another fraction Because I've got another linear factor on bottom x minus two to the first power So I'm gonna have to add another fraction. That's got x plus. Sorry. I keep saying minus two It's plus two on bottom on top, I'm gonna use a different letter for my numbering scheme because I'm starting over with another linear excuse me factor Okay, and I says as I said before We're done creating these partial fractions We have to find a and b. Okay, that's the goal right now is to find a and b so Here's what we're gonna do We are going to multiply by The denominator of the original fraction In factored form might be a little easier Imagine doing that from here to here imagine multiplying both sides by x minus three Times x plus two What's gonna happen? Well, I'll tell you what's gonna happen. What's gonna happen is that the Entire fraction the entire equation is gonna lose all of its denominators It's very easy to see that that happens on the left side because you're multiplying something That's already divided by x minus three times x plus two by x minus three times x plus two So this is gonna delete this and we're just gonna get x plus seven over here, and that's what we want on the other side If we Distribute this in we can see that part of it's gonna cancel so a Times x minus three times x plus two divided by x minus three the x minus three is gonna cancel And you're gonna be left with a times x plus two on top Okay, the other one Multiplying x minus three times x plus two the x plus two is gonna cancel Which is this leaving you with b? x minus three Okay And that's a lot of work. We've got more to do. We've got to do the following we have To distribute these a's and b's to these linear factors that now multiply by them Then we're gonna do a little investigative work with this equation because we've only got one equation We've got two unknowns to solve for So watch this a x plus two a oh Oh Get ahead of myself there a x plus two a plus bx minus 3b like so and What we're gonna do now is we're going to Combine like terms Meaning terms with the same variables. Okay. There are two terms With an x in them on the right and So we are going to combine them like this and factor out that x So there's an ax and a bx That's a plus b times x Then we have plus two a minus 3b not really common at all We'll just stack those in the end. Those are gonna make up a constant. Okay. They're just numbers Now if I'm saying this is equal to x plus seven, I'm actually Implying quite a bit. Okay. What's the coefficient of the x term on the left? It's one This implies because I have only one x term on the right side That a plus b has to equal one This is the first equation that I've created where I can actually solve for a and b But that's not enough because I need to and I only have one. Okay So what we need to do now is We need to set the other portion of This to seven. Okay to a minus 3b Equals seven. Okay. Now. I have the proper number of equations To get a and b to So each time you do a partial fraction decomposition the more complicated what you started with is the more equations You're gonna have but you're gonna be able to solve them as a system like this Sometimes you get some very easily in this case. We're gonna work for it I've got this beautiful system of equations here that's set up just perfectly for elimination as my means of solving And so I'm going to go ahead and multiply the top equation by two s by three Which will give me and I'll write it below 3a plus 3b Equals three like this and I add these two equations the b terms cancel and I get 5a Equals 10 it's 2 a plus 3a is 5a 7 plus 3 is 10 We divide 5 you can see a Equals 2 we found one of those numerators awesome Finding the other one is a cinch you back substitute Take that value got for a and plug it into any of the equations you have here Top one is the easiest imagine it without being multiplied by three You've got a Plus b equals one well now you can substitute in what a is it's two plus b Equals one So if I subtract two then I'll get b b has to equal negative one Okay So I found a and b now you're not done what you got to do is go back up here You got to write The fractions those partial fractions with their found numerators. So a was two and b Was negative one so you could write that instead of plus a negative one you could write minus one over x plus two Now what you want to do obviously is you want to make sure that this is right, okay How can you make sure this is right? Well, you can combine the fractions do the exact reverse Using older maths that you learned years ago. Okay These denominators aren't like so I have to multiply by the lcd We've worked with the lcd enough in the example that you know the lcd is just the combination of these two factors together So the top the first fraction needs the x plus two Because it didn't have it in the lcd The other one needs the x minus three multiplied by it because it didn't have it in the lcd In the lcd. I mean it didn't show it in its denominator That part of the lcd was missing So when you multiply through of course The denominator is x minus three times x plus two. I'm just for time's sake. I'm going to leave it un factored I mean Factor not multiplied out the top is what I care about Two into x plus two. That's two x plus four Now be careful here. This is a minus sign. I have to distribute it To all the terms that follow it. So one times x times a negative is minus x Uh One times negative three times the negative is plus three Now here in this case. We actually do have some like terms Two x minus x is x Four plus three is seven Multiplying the bottom get x squared minus x minus six Which is what you started with so it checks out that this right here Two over x minus three Plot minus one over x plus two is correct Now you're thinking man, I this is crazy. This is so hard. This is so much work I could just guess And figure it out. No, you can't Yes, I can I can factor it and then just split them up and then guess what a and b are No, you can't these are not intuitive numbers It's because of the work required to get to them that you can't just intuitively just Guess what they are you can't okay? So that is not a good strategy A good strategy is this strategy and it's up to you to get used to it so that you're not Lost okay, but takes practice so we're gonna do another one Whoa, look at this guy. This guy is a little bit more complicated. Oh my goodness So if this guy is this complicated Is it a totally different method than before? Hi, I see you. Thanks for joining Ask for any help you need on anything. I'll stop what I'm doing and I'll help you Or bring your friends in I'm here till 11 Pacific standard time so What I want to do Now is step one which again is look here. Is the degree of the numerator Correct Is it smaller than the denominator? Yes, I've got degree two on top with this two here Or degree three on bottom And that means it's a proper fraction again So I don't have to do any long division which would really oof that would be a pain here okay so What we're gonna do is we're going To Back to the denominator. Okay We'll just keep writing the numerator. Don't need to change it the bottom We can factor start by looking at all the terms. Is there something common to every term? We could pull out the greatest common factor Okay, and that's x every term has at least an x in it so that means that x is the greatest common factor I'll factor that out first I have x squared plus 2x plus 1 left Okay Is x squared plus 2x plus 1 irreducible No, it is reducible. Okay, you might not see it But this is a perfect square and now there's ways to tell for example Is the coefficient in the middle Double the final coefficient squared. Yes, that's one way to do it, but you don't have to do it that way you can do this The x method Can I think of two numbers that multiply to one and add to positive two? Yes, of course Can you If you can Good for you. It's one in one Okay Good for you. All right. So that means I can factor the denominator further Which is good because quadratic factors are more work The algebra in this algorithm above is more complicated But doable just more work. Okay So I've got that x there and now instead of writing just x squared plus 2x plus 1. I'm going to write two parentheses Each has an x and each has a plus one from our little Investigation there Okay, so really what I have Are three linear factors, but not really they're the same like I said, it was a perfect square So I shouldn't write it like this I should write it like this Okay, so what I have Is a repeated linear factor whereas before in the previous example I had distinct linear factors Not a problem not a problem at all. Okay So Here's what I'm going to do. I'm going to set this up Now I can think of x as x plus zero. Okay So I'm going to have an a over that x plus zero And I don't need any more copies because it was just the first power Then it's next one I have a linear factor, but I have to to the second power of it So I'm going to have a b1 Or you could write c b and c it actually works. It's a little easier if you do it that way um b over x plus one and then c Over x plus one squared. Why because it was squared here I have to repeatedly write these factors as denominators raising the power until I get to the power of the fully factored denominator original And so I have this here It's now ready To go through and multiply everything by the least common denominator Well, sorry the denominator as it's factored. So I'm going to multiply Everything by x times x plus one squared on the left and the right This is going to cancel over here Only parts of it are going to cancel. So the left side 5x squared plus 20x plus six Set in stone the other side The first fraction a over x the x is going to cancel Leaving us with just a times everything it already didn't have You saw that pattern already and then b One power of x plus one is going to cancel So that b will be multiplied by x times and the other x plus one We'll distribute that then Then c c the x plus one squared will cancel. So we just multiply that by x Okay, a little more work here Now I have to do some foiling and I have to do some multiplication so I can start to Group stuff differently in a way that's helpful like I did in the previous problem So foil here And multiply in by a that's ax squared Plus two ax Plus a for one squared then Bx times x bx squared plus bx Okay, and then cx Okay, like I said before group all like powers of x Okay Don't do anything to the left side yet So and factor out The x squared from them So I've got Two terms with an x squared a and b So that's going to make a plus b x squared after I factor the x squared out Then we've got first power of x terms I've got a two a Plus b plus c x All right, cool And I only have one term without any x's. It's just a oh, that's nice. Okay, you'll see how awesome this is But first you're like, oh my gosh, I have three different letters to solve for I'm gonna have to have three Variables. Oh, no. Yes, you are but that's okay Trust me. This isn't nearly as bad as it looks and you're not going to use elimination to solve it Okay So If the left side equals the right side, we could set coefficients equal to each other just like in the previous problem. Okay What we're going to do at the front is we're going to set five equal to a plus b Five x squared has to equal a plus b x squared Because the power of x the next one's the hard one 20 Equals two a plus b Plus c Oh, dear three variables in that equation The next one Is the simple one the constant terms have to be set equals six equals A. Oh my gosh. I already know what a is a is six Oh, that's so nice Okay So what would I do next if I know that a is six? How would what would I do next I would Find b because the first equation has just a plus b So I will write five equals six plus b Plugging in a And I don't know if you can see that But six plus b equals something less than six five. That means b has to be negative one awesome Okay, and then this isn't so bad now to find c. We just plug a and b into the second equation 20 equals two times six Plus negative one Plus c So 12 minus one. That's 11 20 equals 11 plus c I think you can see right now just with mental math c equals nine Okay All right, we know what a b and c are so we come back To our partial fraction decomposition And we oh, I just realized I scared away that one person Yikes, it's kind of awkward when you're that one person watching someone else's live stream on youtube So if you do that again, sir, I will make sure not to Say hey, buddy. I see you. Hey ask questions. I won't do that to you. That's kind of freaky All right, so come back up here Our partial fraction decomposition Is going to be the following it is going to be six over x And then we've got a negative one for b so minus one over x plus one And then plus c which is nine Over x plus one squared Whoa, that parentheses out of control What is going on there? There we go. I am going to leave it as an exercise to the listener one reader to check this but I can assure you And it's not going to be nearly as easy as the previous one to combine those but you can't do it all right there is my lesson our partial fraction decomposition And it's been about 44 minutes So at this point I would start to wrap up if I'm not getting any questions anymore Just get to a last kind of shout out for any questions we have And um, then I would answer those of course again giving Prefits to the people paying the super chatters So I'm hoping this goes big. I'm hoping people see the use in it I'm going to be able to do this a lot and get a lot of Good usage out of it for people so they can get their questions answered Not just in math, but in sciences writing I'm here to help all around and I'm not going to sit here and say I have all the answers because I don't I might be wrong at times and your feet are correct. Just be respectful.  Um, be kind be professional and let's let's get some let's get some stuff answered. That's why I'm here and This is going to be a really I think a really good thing for youtube If more and more people start doing this, but I'm going to start it. All right And you know, I'm just being facetious. I could be literally the 1500th person to actually do this. We'll see. I just haven't come across it And um, I'm probably the only one doing it with Miro. So we'll we'll see about that Well, like I said guys, um, I would wrap up at this point If I don't have anybody asking any more questions And it's been a pleasure for all of you who are going to see this post And for you one person who I scared off. I love you.  It's just awkward. I get it um, but yeah, guys, I'm Here to help I love helping if I could support my family doing this. I'm certainly gonna try and um Yeah, I love teaching so Teach more people. We'll see what happens. All right guys. Thank you so much for watching It's been Falconator signing out