Answer
$\frac{56-7\sqrt6}{58}$.
Work Step by Step
The given expression is
$=\frac{7}{8-\sqrt6}$
Multiply and divide by the conjugate of the denominator.
$=\frac{7}{8-\sqrt6}\cdot \frac{8+\sqrt6}{8+\sqrt6}$
Use distributive property and the FOIL method.
$=\frac{56+7\sqrt6}{64+8\sqrt6-8\sqrt6+(\sqrt6)(-\sqrt6)}$
Simplify.
$=\frac{56+7\sqrt6}{64-6}$
$=\frac{56-7\sqrt6}{58}$.
