Найдите значение выражения (b+4)/(b^2+16)*((b+4)/(b-4)+(b-4)/(b+4)) при b=3,75.

\[\frac{b + 4}{b^{2} + 16} \cdot \left( \frac{b + 4^{\backslash b + 4}}{b - 4} + \frac{b - 4^{\backslash b - 4}}{b + 4} \right) =\]

\[= \frac{b + 4}{b^{2} + 16} \cdot \frac{b^{2} + 8b + 16 + b^{2} - 8b + 16}{(b - 4)(b + 4)} =\]

\[= \frac{1}{b^{2} + 16} \cdot \frac{2b^{2} + 32}{b - 4} = \frac{2 \cdot \left( b^{2} + 16 \right)}{\left( b^{2} + 16 \right)(b - 4)} =\]

\[= \frac{2}{b - 4}\]

\[b = 3,75:\]

\[\frac{2}{3,75 - 4} = \frac{2}{- 0,25} = - \frac{200}{25} = - 8.\]

\[Ответ:\ - 8.\]