Упростите выражение 7c/(c+2)-(c-8)/(3c+6)*84/(c^2-8c).

Ответ:

\[\frac{7c}{c + 2} - \frac{c - 8}{3c + 6} \cdot \frac{84}{c^{2} - 8c} =\]

\[= \frac{7c}{c + 2} - \frac{(c - 8) \cdot 84}{3(c + 2) \cdot c(c - 8)} =\]

\[= \frac{7c^{\backslash c}}{c + 2} - \frac{28}{c(c + 2)} = \frac{7c^{2} - 28}{c(c + 2)} =\]

\[= \frac{7\left( c^{2} - 4 \right)}{c(c + 2)} = \frac{7(c - 2)(c + 2)}{c(c + 2)} = \frac{7c - 14}{c}\]