Answer
$\dfrac{\sqrt{3z}}{6z}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{1}{\sqrt{12z}}
$ results to
\begin{array}{l}
\dfrac{1}{\sqrt{4\cdot3z}}
\cdot
\dfrac{\sqrt{3z}}{\sqrt{3z}}
\\\\=
\dfrac{\sqrt{3z}}{\sqrt{4\cdot9z^2}}
\\\\=
\dfrac{\sqrt{3z}}{2\cdot3z}
\\\\=
\dfrac{\sqrt{3z}}{6z}
.\end{array}