$\phantom{XX}\dfrac{\sqrt{2}\;+\;\sqrt{3}}{\sqrt{3}}\;=$
$\;=\dfrac{(\sqrt{2}\;+\;\sqrt{3})}{\sqrt{3}}\,\centerdot\,\dfrac{\sqrt{3}}{\sqrt{3}}\;=$
$\;=\dfrac{\sqrt{2}\centerdot\sqrt{3}\;+\;(\sqrt{3})^{\large 2}}{(\sqrt{3})^{\large 2}}\;=$
$\;=\dfrac{\sqrt{6}\;+\;3}{3}\;$