#### Answer

$-\dfrac{\sqrt{6}}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{-3}{\sqrt{6}}
,$ multiply the numerator and the denominator by the denominator.
$\bf{\text{Solution Details:}}$
Multiplying the numerator and the denominator by the denominator, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-3}{\sqrt{6}}\cdot\dfrac{\sqrt{6}}{\sqrt{6}}
\\\\=
\dfrac{-3\sqrt{6}}{(\sqrt{6})^2}
\\\\=
\dfrac{-3\sqrt{6}}{6}
\\\\=
\dfrac{\cancel{3}(-1)\sqrt{6}}{\cancel{3}(2)}
\\\\=
\dfrac{-1\sqrt{6}}{2}
\\\\=
-\dfrac{\sqrt{6}}{2}
.\end{array}