# How do you simplify -20/(sqrt6 - sqrt2)?

Feb 24, 2016

Rationalize the denominator to find that

$- \frac{20}{\sqrt{6} - \sqrt{2}} = - 5 \left(\sqrt{6} + \sqrt{2}\right)$

#### Explanation:

We will use the fact that $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$ to rationalize the denominator.

-20/(sqrt(6)-sqrt(2)) = -(20(sqrt(6)+sqrt(2)))/((sqrt(6)-sqrt(2))(sqrt(6)+sqrt(2))

$= - \frac{20 \left(\sqrt{6} + \sqrt{2}\right)}{{\left(\sqrt{6}\right)}^{2} - {\left(\sqrt{2}\right)}^{2}}$

$= - \frac{20 \left(\sqrt{6} + \sqrt{2}\right)}{6 - 2}$

$= - \frac{20 \left(\sqrt{6} + \sqrt{2}\right)}{4}$

$= - 5 \left(\sqrt{6} + \sqrt{2}\right)$