Answer
$\frac{23\sqrt 5}{30}$
Work Step by Step
As $45=3^2\times5$ and $80=4^2\times5$, we have $\frac{3}{\sqrt 5}-\frac{2}{\sqrt {45}}+\frac{6}{\sqrt {80}}=\frac{3}{\sqrt 5}-\frac{2}{3\sqrt {5}}+\frac{6}{4\sqrt {5}}=\frac{1}{\sqrt 5}(3-\frac{2}{3}+\frac{3}{2})=\frac{23}{6\sqrt 5}=\frac{23\sqrt 5}{30}$
