Take the tour ×  The following expression:   should be
simplified to:   (even if I don't agree that this second is more
simple than the first).  The problem is that I have no idea of
the first step to simplify that.. any help?  share|improve this
question The magic words are "multiply by the conjugate". For
what it is worth, I would actually prefer the former form to the
latter. I find it is easier to keep radicals out of
denominators, so I would call the former the simplification, not
the latter. –  Arturo Magidin Feb 5 '11 at 21:25 I prefer the
latter because the removable singularity is removed. But I also
am prone to say $\sin\frac{\pi}{4}=\frac{1}{\sqrt 2}$ rather
than $\frac{\sqrt 2}{2}$. @Tom: An important use of such
"simplification" is that the latter expression indicates how the
original expression can be continuously extended to $h=0$. This
allows you to determine that the slope of the tangent line to
the curve $y=\sqrt x$ at the point $(4,2)$ is $\frac{1}{4}$. If
you haven't already learned deriva