Докажите тождество (m/(m^2-16m+64)-(m+4)/(m^2-64)):(3m+8)/(m^2-64)=4/(m-8).

\[\left( \frac{m}{m^{2} - 16m + 64} - \frac{m + 4}{m^{2} - 64} \right)\ :\frac{3m + 8}{m^{2} - 64} = \frac{4}{m - 8}\]

\[Упростим\ левую\ часть\ тождества:\ \]

\[\left( \frac{m}{m^{2} - 16m + 64} - \frac{m + 4}{m^{2} - 64} \right)\ :\frac{3m + 8}{m^{2} - 64} =\]

\[= \left( \frac{m^{\backslash m + 8}}{(m - 8)^{2}} - \frac{m + 4^{\backslash m - 8}}{(m - 8)(m + 8)} \right) \cdot \frac{m^{2} - 64}{3m + 8} =\]

\[= \frac{m^{2} + 8m - m^{2} - 4m + 8m + 32}{\left( m^{2} - 64 \right)(m - 8)} \cdot \frac{m^{2} - 64}{3m + 8} =\]

\[= \frac{(12m + 32) \cdot \left( m^{2} - 64 \right)}{\left( m^{2} - 64 \right)(m - 8)(3m + 8)} =\]

\[= \frac{4 \cdot (3m + 8)}{(m - 8)(3m + 8)} = \frac{4}{m - 8}\]

\[\frac{4}{m - 8} = \frac{4}{m - 8}\]

\[Что\ и\ требовалось\ доказать.\]