# How do you rationalize the denominator and simplify 5/(sqrt6+sqrt15)?

Apr 2, 2018

See below

#### Explanation:

$\frac{5}{\sqrt{6} + \sqrt{15}} = \frac{5 \left(\sqrt{6} - \sqrt{15}\right)}{\left(\sqrt{6} + \sqrt{15}\right) \left(\sqrt{6} - \sqrt{15}\right)}$

$= \frac{5 \sqrt{6} - 5 \sqrt{15}}{6 - 15} = \frac{5 \sqrt{6} - 5 \sqrt{15}}{-} 9 = - \frac{5}{9} \left(\sqrt{6} - \sqrt{15}\right)$