Question

Rationalise the denominator and simplify
$\frac{\sqrt{5}}{\sqrt{6}+2}-\frac{\sqrt{5}}{\sqrt{6}-2}$

Answer 1

$\frac{\sqrt{5}}{\sqrt{6}+2}-\frac{\sqrt{5}}{\sqrt{6}-2}$

$\sqrt{5}\left[\frac{\sqrt{6}-2-\sqrt{6}-2}{(\sqrt{6}+2)(\sqrt{6}-2)}\right]$

$\sqrt{5}\left[\frac{-4}{6-4}\right]$

$-2\sqrt{5}$