\[\frac{22}{\sqrt{13} - \sqrt{2}} =\]
\[= \frac{22\left( \sqrt{13} + \sqrt{2} \right)}{\left( \sqrt{13} - \sqrt{2} \right)\left( \sqrt{13} + \sqrt{2} \right)} =\]
\[= \frac{22\left( \sqrt{13} + \sqrt{2} \right)}{13 - 2} =\]
\[= \frac{22}{11}\left( \sqrt{13} + \sqrt{2} \right) = 2\sqrt{13} + 2\sqrt{2}.\]