# How do you rationalize the denominator and simplify 3/(2+sqrt3)?

Mar 28, 2016

$6 - 3 \sqrt{3}$

#### Explanation:

$1$. Multiply the numerator and denominator by the conjugate of $2 + \sqrt{3}$, which is $2 - \sqrt{3}$.

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

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

$2$. Simplify the numerator.

$= \frac{6 - 3 \sqrt{3}}{\left(2 + \sqrt{3}\right) \left(2 - \sqrt{3}\right)}$

$3$. Simplify the denominator.

$= \frac{6 - 3 \sqrt{3}}{4 - 3}$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 6 - 3 \sqrt{3} \textcolor{w h i t e}{\frac{a}{a}} |}}}$