Answer
$-\frac{28+20\sqrt3+7\sqrt5+ 5\sqrt{15}}{26}$.
Work Step by Step
The given expression is
$=\frac{4+\sqrt5}{7-5\sqrt3}$
Multiply and divide by the conjugate of the denominator.
$=\frac{4+\sqrt5}{7-5\sqrt3}\cdot \frac{7+5\sqrt3}{7+5\sqrt3}$
Use the FOIL method.
$=\frac{28+20\sqrt3+7\sqrt5+\sqrt5\cdot 5\sqrt3}{49+35\sqrt3-35\sqrt3+(-5\sqrt3)(5\sqrt3)}$
Simplify.
$=\frac{28+20\sqrt3+7\sqrt5+ 5\sqrt{15}}{49-75}$
$=\frac{28+20\sqrt3+7\sqrt5+ 5\sqrt{15}}{-26}$
$=-\frac{28+20\sqrt3+7\sqrt5+ 5\sqrt{15}}{26}$.
