\[\frac{4}{\sqrt{7} - \sqrt{3}} =\]
\[= \frac{4 \bullet \left( \sqrt{7} + \sqrt{3} \right)}{\left( \sqrt{7} - \sqrt{3} \right)\left( \sqrt{7} + \sqrt{3} \right)} =\]
\[= \frac{4 \bullet \left( \sqrt{7} + \sqrt{3} \right)}{7 - 3} =\]
\[= \frac{4 \bullet \left( \sqrt{7} + \sqrt{3} \right)}{4} = \sqrt{7} + \sqrt{3}\]