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{2cdot(x-1)}{x+1}$$=frac{2x+2-4}{x+1}=2-frac{4}{x+1}$

Answer 2

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