# How do you rationalize the denominator and simplify 3/(sqrt5+sqrt6)?

Apr 18, 2018

We multiply by $\setminus \frac{\sqrt{5} - \sqrt{6}}{\sqrt{5} - \sqrt{6}}$ to rationalize the denominator.

#### Explanation:

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

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

$= \frac{3 \sqrt{5} - 3 \sqrt{6}}{5 - 6}$

$= 3 \sqrt{6} - 3 \sqrt{5}$