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