# How do you rationalize the denominator and simplify (2+sqrt11)/(5-sqrt11)?

Apr 12, 2015

To rationalize a denominator:
Multiply the numerator and denominator by the conjugate of the denominator.

$\frac{2 + \sqrt{11}}{5 - \sqrt{11}} \times \frac{5 + \sqrt{11}}{5 + \sqrt{11}}$

$= \frac{10 + 7 \sqrt{11} + 11}{25 - 11}$

$= \frac{21 + 7 \sqrt{11}}{14}$

$= \frac{3 + \sqrt{11}}{2}$