\[\frac{b - 7^{\backslash b + 7}}{b + 7} - \frac{b^{2} + 49}{b^{2} + 14b + 49} =\]
\[= \frac{b^{2} - 49 - b^{2} - 49}{(b + 7)^{2}} =\]
\[= - \frac{98}{(b + 7)^{2}}.\]