(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

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- Mar 2nd 2010, 05:29 PMbobsanchezFinding the derivative of this function:
(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 - Mar 2nd 2010, 05:57 PMskeeter
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 ...

$\displaystyle \frac{1}{\sqrt{x}(\sqrt{x} + 1)^2}$