Докажите тождество: c^2(c-5)^2*(25-c^2)/(5c+25)+c/(c-5)=-c/5.

\[\frac{c^{2}}{(c - 5)^{2}} \cdot \frac{25 - c^{2}}{5c + 25} + \frac{c}{c - 5} = - \frac{c}{5}\]

\[Преобразуем\ левую\ часть:\]

\[\frac{c^{2}}{(c - 5)^{2}} \cdot \frac{25 - c^{2}}{5c + 25} =\]

\[= \frac{c^{2}(5 - c)(5 + c)}{(5 - c)^{2} \cdot 5(c + 5)} = \frac{c^{2}}{5(5 - c)}\]

\[\frac{c^{2}}{5(5 - c)} - \frac{c^{\backslash 5}}{5 - c} = \frac{c^{2} - 5c}{5(5 - c)} =\]

\[= \frac{- c(5 - c)}{5(5 - c)} = - \frac{c}{5}\]

\[Что\ и\ требовалось\ доказать.\]