(square root of x) - 1/ (square root of x) +1
I know there must be some basic algebra that I'm missing, but I don't know how to handle the square roots. Any help is much appreciated in advance.
Thanks
quotient rule ...
$\displaystyle \frac{d}{dx} \left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)$
$\displaystyle \frac{(\sqrt{x} + 1)\left(\frac{1}{2\sqrt{x}}\right) - (\sqrt{x}-1)\left(\frac{1}{2\sqrt{x}}\right)}{(\sqrt{x} + 1)^2}$
factor the numerator ...
$\displaystyle \frac{\left(\frac{1}{2\sqrt{x}}\right)[(\sqrt{x}+1)- (\sqrt{x}-1)]}{(\sqrt{x} + 1)^2}$
combine like terms in the numerator ...
$\displaystyle \frac{\left(\frac{1}{2\sqrt{x}}\right)[2]}{(\sqrt{x} + 1)^2}$
final version ...
$\displaystyle \frac{1}{\sqrt{x}(\sqrt{x} + 1)^2}$