Fields Medal Prize Winners (1998)


Solving Quadratic Equations by Using the Quadratic Formula
Addition with Negative Numbers
Solving Linear Systems of Equations by Elimination
Rational Exponents
Solving Quadratic Inequalities
Systems of Equations That Have No Solution or Infinitely Many Solutions
Dividing Polynomials by Monomials and Binomials
Polar Representation of Complex Numbers
Solving Equations with Fractions
Quadratic Expressions Completing Squares
Graphing Linear Inequalities
Square Roots of Negative Complex Numbers
Simplifying Square Roots
The Equation of a Circle
Fractional Exponents
Finding the Least Common Denominator
Simplifying Square Roots That Contain Whole Numbers
Solving Quadratic Equations by Completing the Square
Graphing Exponential Functions
Decimals and Fractions
Adding and Subtracting Fractions
Adding and Subtracting Rational Expressions with Unlike Denominators
Quadratic Equations with Imaginary Solutions
Graphing Solutions of Inequalities
FOIL Multiplying Polynomials
Multiplying and Dividing Monomials
Order and Inequalities
Exponents and Polynomials
Variables and Expressions
Multiplying by 14443
Dividing Rational Expressions
Division Property of Radicals
Equations of a Line - Point-Slope Form
Rationalizing the Denominator
Imaginary Solutions to Equations
Multiplying Polynomials
Multiplying Monomials
Adding Fractions
Rationalizing the Denominator
Rational Expressions
Ratios and Proportions
Rationalizing the Denominator
Like Radical Terms
Adding and Subtracting Rational Expressions With Different Denominators
Percents and Fractions
Reducing Fractions to Lowest Terms
Subtracting Mixed Numbers with Renaming
Simplifying Square Roots That Contain Variables
Factors and Prime Numbers
Rules for Integral Exponents
Multiplying Monomials
Graphing an Inverse Function
Factoring Quadratic Expressions
Solving Quadratic Inequalities
Factoring Polynomials
Multiplying Radicals
Simplifying Fractions 1
Graphing Compound Inequalities
Rationalizing the Denominator
Simplifying Products and Quotients Involving Square Roots
Standard Form of a Line
Multiplication by 572
Adding and Subtracting Fractions
Multiplying Polynomials
Factoring Trinomials
Solving Exponential Equations
Solving Equations with Fractions
Simplifying Complex Fractions
Multiplying and Dividing Fractions
Mathematical Terms
Solving Quadratic Equations by Factoring
Factoring General Polynomials
Adding Rational Expressions with the Same Denominator
The Trigonometric Functions
Solving Nonlinear Equations by Factoring
Solving Systems of Equations
Midpoint of a Line Segment
Complex Numbers
Graphing Systems of Equations
Reducing Rational Expressions
Rewriting Algebraic Fractions
Rationalizing the Denominator
Adding, Subtracting and Multiplying Polynomials
Radical Notation
Solving Radical Equations
Positive Integral Divisors
Solving Rational Equations
Rational Exponents
Mathematical Terms
Rationalizing the Denominator
Subtracting Rational Expressions with the Same Denominator
Axis of Symmetry and Vertex of a Parabola
Simple Partial Fractions
Simplifying Radicals
Powers of Complex Numbers
Fields Medal Prize Winners (1998)

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Solving Equations with Fractions

After studying this lesson, you will be able to:

  • Solve equations containing fractions.

To Solve Equations containing fractions:

Clear out the fractions by multiplying the ENTIRE equation by the common denominator.



Sometimes when dealing with equations, all the variable cancel out. When this happens we have a "special case". If the expression we're left with is a true mathematical statement, our solution is called the Identity Property which means that there is an infinite number of solutions. The symbol for infinity is . If the expression we're left with is a false mathematical statement, there will be no solution. We indicate this with the empty set symbol which is Ã˜.


Example 1

2x + 5 = 2x -3 To solve this equation, we need to attempt to get the variables together on the same side.
2x + 5 - 2x = 2x -3 - 2x When we subtract 2x from each side, all variables are eliminated, leaving us with 5 = -3
5 = -3 We know this is a "special case" since we have no variables. Since 5 is not equal to -3, this is a false statement. Therefore there are no solutions.
Ã˜ We write the empty set symbol for our answer


Example 2

3 ( x + 1 ) - 5 = 3x -2 To solve this equation, we first remove the parentheses by distributing.
3x + 3 - 5 = 3x - 2 We need to collect like terms (3 - 5 ) on the left side
3x - 2 = 3x -2 To solve this equation, we need to attempt to get the variables together on the same side.
3x - 2 - 3x = 3x -2 - 3x We do this by subtracting 3x from each side.

This gives us -2 = -2

-2 = -2 We know this is a "special case" since we have no variables. Since -2 is equal to -32, this is a true statement (the identity property). Therefore there are infinite number of solutions.
We write the symbol for infinity for our answer