# How do you rationalize the denominator and simplify 6/(3-sqrt11)?

Aug 31, 2016

$\frac{6}{3 - \sqrt{11}} = - 9 - 3 \sqrt{11}$

#### Explanation:

Multiply both numerator and denominator by the radical conjugate $3 + \sqrt{11}$ of the denominator, then simplify...

$\frac{6}{3 - \sqrt{11}} = \frac{6 \left(3 + \sqrt{11}\right)}{\left(3 - \sqrt{11}\right) \left(3 + \sqrt{11}\right)}$

$\textcolor{w h i t e}{\frac{6}{3 - \sqrt{11}}} = \frac{6 \left(3 + \sqrt{11}\right)}{{3}^{2} - {\left(\sqrt{11}\right)}^{2}}$

$\textcolor{w h i t e}{\frac{6}{3 - \sqrt{11}}} = \frac{6 \left(3 + \sqrt{11}\right)}{9 - 11}$

$\textcolor{w h i t e}{\frac{6}{3 - \sqrt{11}}} = - 3 \left(3 + \sqrt{11}\right)$

$\textcolor{w h i t e}{\frac{6}{3 - \sqrt{11}}} = - 9 - 3 \sqrt{11}$