# Rationalize (sqrt(6) + sqrt(5))/(sqrt(5) - sqrt(3))?

Apr 15, 2017

Multiply the fraction with the "opposite" (the denominator with the reverse sign) of the denominator and simplify.

#### Explanation:

$\frac{\sqrt{6} + \sqrt{5}}{\sqrt{5} - \sqrt{3}} \cdot \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}}$

Simplifying, we get:
$\frac{\sqrt{30} + \sqrt{18} + \sqrt{15} + 5}{5 + \sqrt{15} - \sqrt{15} - 3}$

$\to \frac{\sqrt{30} + \sqrt{18} + \sqrt{15} + 5}{2}$

$= \frac{\sqrt{30} + \sqrt{18} + \sqrt{15} + 5}{2}$