Answer
$\frac{-3\sqrt{10}+3\sqrt{5}}{5}$.
Work Step by Step
The given expression is
$=\frac{-3}{\sqrt{10}+\sqrt{5}}$
Multiply the numerator and denominator by the conjugate of the denominator.
$=\frac{-3}{\sqrt{10}+\sqrt{5}}\cdot \frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}-\sqrt{5}}$
Multiply in the denominator.
$=\frac{-3(\sqrt{10}-\sqrt{5})}{10-5}$
Simplify the denominator.
$=\frac{-3(\sqrt{10}-\sqrt{5})}{5}$
Clear the parentheses in the numerator.
$=\frac{-3\sqrt{10}+3\sqrt{5}}{5}$.
