Answer
$\frac{5+\sqrt{3}}{11}$
Work Step by Step
The given expression is
$=\frac{2}{5-\sqrt{3}}$
The conjugate of $5-\sqrt{3}$ is $5+\sqrt{3}$
$=\frac{2}{5-\sqrt{3}} \cdot \frac{5+\sqrt{3}}{5+\sqrt{3}}$
Use sum and difference pattern.
$=\frac{2(5+\sqrt{3})}{5^2-(\sqrt{3})^2}$
Simplify.
$=\frac{2(5+\sqrt{3})}{25-3}$
$=\frac{2(5+\sqrt{3})}{22}$
$=\frac{5+\sqrt{3}}{11}$
