\[\frac{b}{b - 16} - \frac{\sqrt{b}}{\sqrt{b} + 4} =\]
\[= \frac{b}{\left( \sqrt{b} - 4 \right)\left( \sqrt{b} + 4 \right)} - \frac{\sqrt{b}}{\sqrt{b} + 4} =\]
\[= \frac{b - \sqrt{b}\left( \sqrt{b} - 4 \right)}{\left( \sqrt{b} - 4 \right)\left( \sqrt{b} + 4 \right)} =\]
\[= \frac{b - b + 4\sqrt{b}}{b - 16} = \frac{4\sqrt{b}}{b - 16\ }\]