# How do you rationalize the denominator and simplify (5+sqrt3)/(2-sqrt3)?

Dec 21, 2016

$\textcolor{g r e e n}{13 + 7 \sqrt{3}}$

#### Explanation:

We can rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.

The conjugate of $\left(2 - \sqrt{3}\right)$ is $\left(2 + \sqrt{3}\right)$

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

$\textcolor{w h i t e}{\text{XXX}} = \frac{13 + 7 \sqrt{3}}{{2}^{2} - {\left(\sqrt{3}\right)}^{2}} = 13 + 7 \sqrt{3}$