\[\frac{18}{\sqrt{13} + 2} = \frac{18\left( \sqrt{13} - 2 \right)}{\left( \sqrt{13} + 2 \right)\left( \sqrt{13} - 2 \right)} =\]
\[= \frac{18\left( \sqrt{13} - 2 \right)}{13 - 4} = \frac{18\left( \sqrt{13} - 2 \right)}{9} =\]
\[= 2\left( \sqrt{13} - 2 \right)\]