# How do you rationalize the denominator and simplify (sqrt(11)-sqrt(2))/(sqrt(11)+sqrt(2))?

Apr 3, 2018

$\frac{13 - 2 \sqrt{22}}{9}$
$\frac{\sqrt{11} - \sqrt{2}}{\sqrt{11} + \sqrt{2}}$
=$\frac{\sqrt{11} - \sqrt{2}}{\sqrt{11} + \sqrt{2}} \times \frac{\sqrt{11} - \sqrt{2}}{\sqrt{11} - \sqrt{2}}$
=$\left(\frac{11 - 2 \sqrt{22} + 2}{11 - 2}\right)$
=$\frac{13 - 2 \sqrt{22}}{9}$