Answer
$-\frac{16-9\sqrt3}{13}$.
Work Step by Step
The given expression is
$=\frac{\sqrt3-2}{2\sqrt3+5}$
The conjugate of the denominator is $2\sqrt3-5$.
Multiply the numerator and the denominator by $2\sqrt3-5$.
$=\frac{\sqrt3-2}{2\sqrt3+5}\cdot \frac{2\sqrt3-5}{2\sqrt3-5}$
Use FOIL in the numerator and the special formula $(A+B)(A-B)=A^2-B^2$ in the denominator.
$=\frac{\sqrt3\cdot 2\sqrt3-5\sqrt3-2\cdot 2\sqrt3+5\cdot 2}{(2\sqrt3)^2-5^2}$
Use product rule.
$=\frac{6-5\sqrt3-4\sqrt3+10}{12-25}$
Simplify.
$=\frac{16-9\sqrt3}{-13}$
$=-\frac{16-9\sqrt3}{13}$.
