# How do you rationalize the denominator and simplify your answer 3/(2 + sqrt(12))?

Apr 11, 2015

To rationalize the denominator multiply both the numerator and the denominator by the conjugate of the denominator

$\frac{3}{2 + \sqrt{12}}$

$= \frac{3}{2 + \sqrt{12}} \times \frac{2 - \sqrt{12}}{2 - \sqrt{12}}$

$= \frac{6 - 3 \sqrt{12}}{4 - 12}$

$= \frac{6 - 6 \sqrt{3}}{- 8}$

$= \frac{3}{4} \left(\sqrt{3} - 1\right)$