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

Jan 24, 2017

$7 + 4 \sqrt{3}$

#### Explanation:

Since

$\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$,

you would multiply both the terms of the fraction by

$2 + \sqrt{3}$,

then you get the expression:

$\frac{\left(2 + \sqrt{3}\right) \textcolor{red}{\left(2 + \sqrt{3}\right)}}{\left(2 - \sqrt{3}\right) \textcolor{red}{\left(2 + \sqrt{3}\right)}}$

that's

$\frac{4 + 4 \sqrt{3} + 3}{4 - 3} = 7 + 4 \sqrt{3}$