Question

Упростить выражение:\left( {\frac{2}{{{x^2} - 1}} + \frac{1}{{x + 1}}} \right)({x^2} - x) - x

Answer 1

$\left( {\frac{2}{{{x^2} - 1}} + \frac{1}{{x + 1}}} \right)({x^2} - x) - x=\left( {\frac{2}{{(x - 1)(x+1)}} + \frac{1}{{x + 1}}} \right)({x^2} - x) - x=\\ =\left( {\frac{2}{{(x-1)(x+1)}} + \frac{x-1}{{(x-1)(x + 1)}}} \right)({x^2} - x) - x = \frac{(x+1)\cdot x(x-1)}{(x-1)(x+1)}-x= \\ =x-x=0$