Answer
$\displaystyle \frac{-\sqrt{6}}{4}$
Work Step by Step
We rationalize the denominator:
$\displaystyle \frac{-\sqrt{3}}{\sqrt{8}}=\frac{-\sqrt{3}\sqrt{8}}{\sqrt{8}\sqrt{8}}=\frac{-\sqrt{24}}{8}=\frac{-\sqrt{4*6}}{8}=\frac{-2\sqrt{6}}{8}=\frac{-\sqrt{6}}{4}$
