Answer
$10-5\sqrt3$.
Work Step by Step
The given expression is
$=\frac{5}{2+\sqrt3}$
Multiply and divide by the conjugate of the denominator.
$=\frac{5}{2+\sqrt3}\cdot \frac{2-\sqrt3}{2-\sqrt3}$
Use distributive property and the FOIL method.
$=\frac{10-5\sqrt3}{4+2\sqrt3-2\sqrt3+(\sqrt3)(-\sqrt3)}$
Simplify.
$=\frac{10-5\sqrt3}{4-3}$
$=\frac{10-5\sqrt3}{1}$
$=10-5\sqrt3$.
