# How do you rationalize the denominator and simplify 5/(sqrt[3] – sqrt[5])?

Mar 17, 2016

$\frac{5}{\sqrt{3} - \sqrt{5}} = - \frac{5}{2} \left(\sqrt{3} + \sqrt{5}\right)$

#### Explanation:

Multiply both numerator and denominator by $\left(\sqrt{3} + \sqrt{5}\right)$:

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

=(5(sqrt(3)+sqrt(5)))/((sqrt(3)-sqrt(5))(sqrt(3)+sqrt(5))

$= \frac{5 \left(\sqrt{3} + \sqrt{5}\right)}{{\left(\sqrt{3}\right)}^{2} - {\left(\sqrt{5}\right)}^{2}}$

$= \frac{5 \left(\sqrt{3} + \sqrt{5}\right)}{3 - 5}$

$= \frac{5 \left(\sqrt{3} + \sqrt{5}\right)}{- 2}$

$= - \frac{5}{2} \left(\sqrt{3} + \sqrt{5}\right)$