Answer
$\dfrac{2}{\sqrt{6x}}$
Work Step by Step
Rationalizing the numerator, the given expression, $
\dfrac{\sqrt{8}}{2\sqrt{3x}}
,$ is equivalent to
\begin{array}{l}
\dfrac{\sqrt{8}}{2\sqrt{3x}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}
\\\\=
\dfrac{\sqrt{16}}{2\sqrt{6x}}
\\\\=
\dfrac{4}{2\sqrt{6x}}
\\\\=
\dfrac{2}{\sqrt{6x}}
.\end{array}