Упростите выражение: (1/(c^2-2cd+d^2)-1/(c^2-d^2)):(4d/(c^4-c^2*d^2).

Ответ:

\[\left( \frac{1}{c^{2} - 2cd + d^{2}} - \frac{1}{c^{2} - d^{2}} \right)\ :\frac{4d}{c^{4} - c^{2}d^{2}} =\]

\[= \left( \frac{1^{\backslash c + d}}{(c - d)^{2}} - \frac{1^{\backslash c - d}}{(c - d)(c + d)} \right) \cdot \frac{c^{4} - c^{2}d^{2}}{4d} =\]

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

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

\[= \frac{c^{2}}{2c + 2d}.\]