\[\frac{35}{\sqrt{37} + \sqrt{2}} =\]
\[= \frac{35 \cdot \left( \sqrt{37} - \sqrt{2} \right)}{\left( \sqrt{37} + \sqrt{2} \right)\left( \sqrt{37} - \sqrt{2} \right)} =\]
\[= \frac{35 \cdot \left( \sqrt{37} - \sqrt{2} \right)}{37 - 2} =\]
\[= \frac{35 \cdot (\sqrt{37} - \sqrt{2})}{35} = \sqrt{37} - \sqrt{2}\]