Answer
$\dfrac{5\sqrt{5}}{12}$
Work Step by Step
Using the properties of radicals, the expression $
\dfrac{\sqrt{45}}{4}-\dfrac{\sqrt{5}}{3}
$ simplifies to
\begin{array}{l}
\dfrac{\sqrt{9\cdot5}}{4}-\dfrac{\sqrt{5}}{3}
\\\\=
\dfrac{3\sqrt{5}}{4}-\dfrac{\sqrt{5}}{3}
\\\\=
\dfrac{3(3\sqrt{5})-4(\sqrt{5})}{12}
\\\\=
\dfrac{9\sqrt{5}-4\sqrt{5}}{12}
\\\\=
\dfrac{5\sqrt{5}}{12}
.\end{array}
