\[\frac{\sqrt{30} + \sqrt{35}}{\sqrt{12} + \sqrt{14}} = \frac{\sqrt{5}\left( \sqrt{6} + \sqrt{7} \right)}{\sqrt{2}\left( \sqrt{6} + \sqrt{7} \right)} =\]
\[= \frac{\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{5 \cdot 2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{10}}{2}.\]