Answer
$\frac{15-3\sqrt{3}}{11}$
Work Step by Step
The given expression is
$=\frac{6}{5+\sqrt{3}}$
The conjugate of $5+\sqrt{3}$ is $5-\sqrt{3}$
$=\frac{6}{5+\sqrt{3}} \cdot \frac{5-\sqrt{3}}{5-\sqrt{3}}$
Use sum and difference pattern.
$=\frac{6(5-\sqrt{3})}{5^2-(\sqrt{3})^2}$
Simplify.
$=\frac{6(5-\sqrt{3})}{25-3}$
$=\frac{6(5-\sqrt{3})}{22}$
$=\frac{3(5-\sqrt{3})}{11}$
Use distributive property.
$=\frac{15-3\sqrt{3}}{11}$
