Упростите выражение: ((c-2)/(c+2)-c/(c-2))*((c+2)/(2-3c)).

Ответ:

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

\[= \frac{c^{2} - 4c + 4 - c^{2} - 2c}{(c + 2)(c - 2)} \cdot \frac{c + 2}{2 - 3c} =\]

\[= \frac{4 - 6c}{c - 2} \cdot \frac{1}{2 - 3c} =\]

\[= \frac{2 \cdot (2 - 3c)}{(c - 2)(2 - 3c)} = \frac{2}{c - 2}.\]