Answer
$\frac{6\sqrt{5}-5}{31}$
Work Step by Step
The given expression is
$=\frac{\sqrt{5}}{6+\sqrt{5}}$
The conjugate of $6+\sqrt{5}$ is $6-\sqrt{5}$
$=\frac{\sqrt{5}}{6+\sqrt{5}} \cdot \frac{6-\sqrt{5}}{6-\sqrt{5}}$
Use sum and difference pattern.
$=\frac{\sqrt{5}(6-\sqrt{5})}{6^2-(\sqrt{5})^2}$
Simplify.
$=\frac{6\sqrt{5}-\sqrt{5}\cdot \sqrt{5}}{36-5}$
$=\frac{6\sqrt{5}-5}{31}$
