\[\frac{14}{\sqrt{17} + \sqrt{3}} =\]
\[= \frac{14 \cdot \left( \sqrt{17} - \sqrt{3} \right)}{\left( \sqrt{17} + \sqrt{3} \right)\left( \sqrt{17} - \sqrt{3} \right)} =\]
\[= \frac{14 \cdot \left( \sqrt{17} - \sqrt{3} \right)}{17 - 3} =\]