Answer
$\dfrac{13\sqrt{15}}{15}$
Work Step by Step
$\displaystyle \sqrt{\frac{5}{3}}=\sqrt{\frac{25}{15}}=\frac{\sqrt{25}}{\sqrt{15}}=\frac{5}{\sqrt{15}}\color{red}{ \cdot\frac{ \sqrt{15}}{\sqrt{15}} }= \frac{5\sqrt{15}}{15}=3\sqrt{15}$
$\displaystyle \sqrt{\frac{3}{5}}=\sqrt{\frac{9}{15}}=\frac{\sqrt{9}}{\sqrt{15}}=\frac{3}{\sqrt{15}}\color{red}{ \cdot\frac{ \sqrt{15}}{\sqrt{15}} }=\frac{3\sqrt{15}}{15}$
$\displaystyle \sqrt{15}-\sqrt{\frac{5}{3}}+\sqrt{\frac{3}{5}}= \frac{15\sqrt{15}}{15}-\frac{5\sqrt{15}}{15}+\frac{3\sqrt{15}}{15}\\\\\\=\dfrac{13\sqrt{15}}{15}$
