\[\frac{4}{\sqrt{13} - 3} = \frac{4 \cdot \left( \sqrt{13} + 3 \right)}{\left( \sqrt{13} - 3 \right)\left( \sqrt{13} + 3 \right)} =\]
\[= \frac{4 \cdot \left( \sqrt{13} + 3 \right)}{13 - 9} = \frac{4 \cdot \left( \sqrt{13} + 3 \right)}{4} =\]
\[= \sqrt{13} + 3\]