Упростите выражение: (c^0,5/(c^0,5-d^0,5)-d/(c-c^0,5*d^0,5))*(5c^1,5)/(c^0,5+d^0,5).

Ответ:

\[\left( \frac{c^{0,5}}{c^{0,5} - d^{0,5}} - \frac{d}{c - c^{0,5}d^{0,5}} \right) \cdot \frac{5c^{1,5}}{c^{0,5} + d^{0,5}} = 5\]

\[1)\ \frac{c^{0,5}}{c^{0,5} - d^{0,5}} - \frac{d}{c - c^{0,5}d^{0,5}} =\]

\[= \frac{{c^{0,5}}^{\backslash c^{0,5}}}{c^{0,5} - d^{0,5}} - \frac{d}{c^{0,5}\left( c^{0,5} - d^{0,5} \right)} =\]

\[= \frac{c - d}{c^{0,5}\left( c^{0,5} - d^{0,5} \right)} =\]

\[= \frac{\left( c^{0,5} + d^{0,5} \right)\left( c^{0,5} - d^{0,5} \right)}{c^{0,5}\left( c^{0,5} - d^{0,5} \right)} =\]

\[= \frac{c^{0,5} + d^{0,5}}{c^{0,5}};\]

\[2)\ \frac{c^{0,5} + d^{0,5}}{c^{0,5}} \cdot \frac{5c^{1,5}}{c^{0,5} + d^{0,5}} = 5.\]