Answer
$\frac{10+2\sqrt7+5\sqrt3+\sqrt{21}}{18}$.
Work Step by Step
The given expression is
$=\frac{2+\sqrt3}{5-\sqrt7}$
Multiply and divide by the conjugate of the denominator.
$=\frac{2+\sqrt3}{5-\sqrt7}\cdot \frac{5+\sqrt7}{5+\sqrt7}$
Use the FOIL method.
$=\frac{10+2\sqrt7+5\sqrt3+\sqrt3\cdot \sqrt7}{25+5\sqrt7-5\sqrt7+(\sqrt7)(-\sqrt7)}$
Simplify.
$=\frac{10+2\sqrt7+5\sqrt3+\sqrt{21}}{25-7}$
$=\frac{10+2\sqrt7+5\sqrt3+\sqrt{21}}{18}$.
