# How do you rationalize the denominator and simplify 3/(2+sqrt12)?

Apr 23, 2016

$\frac{3}{\sqrt{12} + 2} = \frac{3}{\sqrt{12} + 2} \times \frac{\sqrt{12} - 2}{\sqrt{12} - 2}$
$= \frac{3 \sqrt{{2}^{2} \times 3} - 6}{12 - 2} = \frac{6 \sqrt{3} - 6}{10} = \frac{6}{10} \times \left(\sqrt{3} - 1\right)$
$= \frac{3}{5} \times \left(\sqrt{3} - 1\right)$