Answer
$\frac{3\sqrt 5-2\sqrt 3+3\sqrt {15}-6}{33}$
Work Step by Step
Multiply $\frac{3\sqrt 5-2\sqrt 3}{3\sqrt 5-2\sqrt 3}$ to the expression, we have:
$\frac{1+\sqrt 3}{3\sqrt 5+2\sqrt 3}\cdot \frac{3\sqrt 5-2\sqrt 3}{3\sqrt 5-2\sqrt 3}=\frac{3\sqrt 5-2\sqrt 3+3\sqrt {15}-6}{45-12}=\frac{3\sqrt 5-2\sqrt 3+3\sqrt {15}-6}{33}$
