# How do you simplify 9/(sqrt6 - sqrt5)?

Jun 16, 2018

This problem can be solved by using using the conjugate of the denominator and rationalization

#### Explanation:

$\setminus \frac{9}{\setminus \sqrt{6} - \setminus \sqrt{5}}$

$= \frac{9}{\setminus \sqrt{6} - \setminus \sqrt{5}} \cdot \frac{\setminus \sqrt{6} + \setminus \sqrt{5}}{\setminus \sqrt{6} + \setminus \sqrt{5}}$

$= \frac{9 \cdot \left(\setminus \sqrt{6} + \setminus \sqrt{5}\right)}{{\left(\setminus \sqrt{6}\right)}^{2} - {\left(\setminus \sqrt{5}\right)}^{2}}$

$= \frac{9 \cdot \left(\setminus \sqrt{6} + \setminus \sqrt{5}\right)}{6 - 5} = 9 \cdot \left(\setminus \sqrt{6} + \setminus \sqrt{5}\right)$