# How do you rationalize the denominator and simplify (2+ sqrt 3)/(5- sqrt 3)?

May 30, 2016

$\frac{7 \sqrt{3} + 13}{22}$

#### Explanation:

Given,

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

Multiply the numerator and denominator by the conjugate of the denominator.

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

Simplify.

$= \frac{10 + 2 \sqrt{3} + 5 \sqrt{3} + 3}{25 - 3}$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{7 \sqrt{3} + 13}{22}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$