x^2 / (Square Root(x+1)) - (Square Root(x-1))

How to I multiply the conjugate on the bottom? I really just don't know how to do it

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- Feb 2nd 2009, 08:01 AMDicksonRationalizing the Denominator
x^2 / (Square Root(x+1)) - (Square Root(x-1))

How to I multiply the conjugate on the bottom? I really just don't know how to do it - Feb 2nd 2009, 08:13 AMmathaddictRe :
$\displaystyle

\frac{x^2}{\sqrt{x+1}-\sqrt{x-1}}$

Multiply the top and bottom by $\displaystyle \frac{\sqrt{x+1}+\sqrt{x-1}}{\sqrt{x+1}+\sqrt{x-1}}$

and hence it equals $\displaystyle \frac{x^2}{2}(\sqrt{x+1}+\sqrt{x-1})$

Use $\displaystyle (a+b)(a-b)=a^2-b^2$