#### Answer

$\dfrac{\sqrt{21}}{8}$

#### Work Step by Step

Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $
\dfrac{3\sqrt{7}}{4\sqrt{12}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3\sqrt{7}}{4\sqrt{12}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}
\\\\=
\dfrac{3\sqrt{21}}{4\sqrt{36}}
\\\\=
\dfrac{3\sqrt{21}}{4\sqrt{(6)^2}}
\\\\=
\dfrac{3\sqrt{21}}{4\cdot6}
\\\\=
\dfrac{\cancel{3}\sqrt{21}}{4\cdot\cancel{3}(2)}
\\\\=
\dfrac{\sqrt{21}}{8}
.\end{array}