Answer
$\dfrac{3\sqrt{2}}{5}$
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{6\sqrt{12}}{5\sqrt{24}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{6}{5}\sqrt{\dfrac{12}{24}}
\\\\=
\dfrac{6}{5}\sqrt{\dfrac{1}{2}}
\\\\=
\dfrac{6}{5}\sqrt{\dfrac{1}{2}\cdot\dfrac{2}{2}}
\\\\=
\dfrac{6}{5}\sqrt{\dfrac{2}{4}}
\\\\=
\dfrac{6}{5}\cdot\dfrac{\sqrt{2}}{\sqrt{4}}
\\\\=
\dfrac{6}{5}\cdot\dfrac{\sqrt{2}}{\sqrt{(2)^2}}
\\\\=
\dfrac{6}{5}\cdot\dfrac{\sqrt{2}}{2}
\\\\=
\dfrac{\cancel{2}(3)}{5}\cdot\dfrac{\sqrt{2}}{\cancel{2}}
\\\\=
\dfrac{3\sqrt{2}}{5}
.\end{array}
