# How do you rationalize the denominator and simplify 1/(sqrt3-sqrt5)?

Sep 11, 2016

The expression can be simplified to $- \frac{\sqrt{3} + \sqrt{5}}{2}$.

#### Explanation:

Multiply the entire expression by the conjugate of the denominator. The conjugate can be found by switching the middle sign in the denominator (when the denominator is a binomial , of course).

$\implies \frac{1}{\sqrt{3} - \sqrt{5}} \times \frac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}}$

$\implies \frac{\sqrt{3} + \sqrt{5}}{\sqrt{9} - \sqrt{25}}$

$\implies \frac{\sqrt{3} + \sqrt{5}}{3 - 5}$

$\implies \frac{\sqrt{3} + \sqrt{5}}{- 2}$

$\implies - \frac{\sqrt{3} + \sqrt{5}}{2}$

Hopefully this helps!