Answer
$\dfrac{5\sqrt6}{6}$
Work Step by Step
Rationalize each denominator to obtain:
\begin{align*}
&=\frac{\sqrt{2}}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}+\frac{\sqrt{3}}{\sqrt2}\cdot \frac{\sqrt2}{\sqrt2}\\\\
&=\frac{\sqrt6}{3}+\frac{\sqrt6}{2}
\end{align*}
Make the expressions similar using their LCD which is $6$ to obtain:
\begin{align*}
&=\frac{\sqrt6 \cdot 2}{3\cdot 2}+\frac{\sqrt6\cdot 3}{2\cdot 3}\\\\
&=\frac{2\sqrt6}{6}+\frac{3\sqrt6}{6}\\\\
&=\frac{(2+3)\sqrt6}{6}\\\\
&=\frac{5\sqrt6}{6}
\end{align*}
