\[\frac{8}{b^{2} - 25} - \frac{4}{b^{2} + 5b} =\]
\[= \frac{8^{\backslash b}}{(b - 5)(b + 5)} - \frac{4^{\backslash b - 5}}{b(b + 5)} =\]
\[= \frac{8b - 4 \cdot (b - 5)}{b(b - 5)(b + 5)} =\]
\[= \frac{8b - 4b + 20}{b(b - 5)(b + 5)} =\]
\[= \frac{4b + 20}{b(b - 5)(b + 5)} =\]