Answer
$\dfrac{-\sqrt{6}}{4}$
Work Step by Step
We rationalize the denominator by multiplying both numerator and denominator by $\sqrt 8$:
$$\require{cancel}
\frac{-\sqrt 3}{\sqrt 8}=\frac{-\sqrt 3\sqrt 8}{\sqrt 8 \sqrt 8}=\frac{-\sqrt{24}}{8}=\frac{-\sqrt{4\times6}}{8}=\frac{-2\sqrt6}{8}=\frac{-\cancel{2}\sqrt6}{\cancel{8}\color{blue}4}=\frac{-\sqrt{6}}{4}
.$$
