Упростите выражение: (6c^3+3c)/(c^3-1)-3c^2/(c^2+c+1).

Ответ:

\[\frac{6c^{3} + 3c}{c^{3} - 1} - \frac{3c^{2}}{c^{2} + c + 1} =\]

\[= \frac{6c^{3} + 3c}{(c - 1)\left( c^{2} + c + 1 \right)} - \frac{3c^{2}}{c^{2} + c + 1} =\]

\[= \frac{6c^{3} + 3c - 3c^{2}(c - 1)}{(c - 1)\left( c^{2} + c + 1 \right)} =\]

\[= \frac{6c^{3} + 3c - 3c^{3} + 3c^{2}}{(c - 1)\left( c^{2} + c + 1 \right)} =\]

\[= \frac{3c^{3} + 3c^{2} + 3c}{(c - 1)\left( c^{2} + c + 1 \right)} =\]

\[= \frac{3c(c^{2} + c + 1)}{(c - 1)(c^{2} + c + 1)} = \frac{3c}{c - 1}.\]