Question

Упростите выражение (1/х-1 - 1/х+1) * (х-1)в квадрате

Answer 1

$\displaystyle \left(\frac{1}{x-1}-\frac{1}{x+1}\right)\cdot (x-1)^2=\frac{x+1-x+1}{(x-1)(x+1)} (x-1)^2=\frac{2\cdot(x-1)}{x+1}$$=\frac{2x+2-4}{x+1}=2-\frac{4}{x+1}$

Answer 2

$(\frac{1}{x-1}-\frac{1}{x+1})*(x-1)^2=(\frac{1(x+1)}{(x+1)(x-1)}-\frac{1(x-1)}{(x+1)(x-1)})*(x-1)^2=\\\frac{x+1-(x-1)}{(x+1)(x-1)}*(x-1)^2=\frac{2}{x+1}*(x-1)=\frac{2x-2}{x+1}$