\[\frac{7 + \sqrt{7}}{\sqrt{14} + \sqrt{2}} = \frac{\sqrt{7}\left( \sqrt{7} + 1 \right)}{\sqrt{2}\left( \sqrt{7} + 1 \right)} =\]
\[= \frac{\sqrt{7}}{\sqrt{2}} = \sqrt{\frac{7}{2}} = \sqrt{3,5}.\]