Упростите выражение: (x/(x-1)-x/(x+1)-(x^2+1)/(1-x^2)):(x^2+x)/(x-1)^2.

\[\left( \frac{x^{\backslash x + 1}}{x - 1} - \frac{x^{\backslash x - 1}}{x + 1} - \frac{x^{2} + 1^{\backslash - 1}}{1 - x^{2}} \right)\ :\frac{x^{2} + x}{(x - 1)^{2}} =\]

\[= \frac{x^{2} + x - x^{2} + x + x^{2} + 1}{(x - 1)(x + 1)} \cdot \frac{(x - 1)^{2}}{x^{2} + x} =\]

\[= \frac{x^{2} + 2x + 1}{x + 1} \cdot \frac{x - 1}{x(x + 1)} =\]

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