\[\frac{c}{c - 4} - \frac{\sqrt{c}}{\sqrt{c} - 2} =\]
\[= \frac{c}{\left( \sqrt{c} - 2 \right)\left( \sqrt{c} + 2 \right)} - \frac{\sqrt{c}}{\sqrt{c} - 2} =\]
\[= \frac{c - \sqrt{c} \cdot \left( \sqrt{c} + 2 \right)}{\left( \sqrt{c} - 2 \right)\left( \sqrt{c} + 2 \right)} =\]
\[= \frac{c - c - 2\sqrt{c}}{c - 4} = - \frac{2\sqrt{c}}{c - 4} = \frac{2\sqrt{c}}{4 - c}\]