Đáp án+Giải thích các bước giải:
$\left \{ {{2x-2=2(x-1)} \atop {x^2-1=(x-1)(x+1)}} \right.$
$⇔MTC=2(x-1)(x+1)$
$*)\dfrac{x+1}{2x-2}+ \dfrac{-2x}{x^2-1}$
$=\dfrac{x+1}{2(x-1)}+\dfrac{-2x}{(x-1)(x+1)}$
$=\dfrac{(x+1)(x+1)}{2(x-1)(x+1)}+\dfrac{2(-2x)}{2(x-1)(x+1)}$
$=\dfrac{(x+1)^2-4x}{2(x-1)(x+1)}$
$=\dfrac{x^2-2x+1}{2(x-1)(x+1)}$
$=\dfrac{(x-1)^2}{2(x-1)(x+1)}$
$=\dfrac{x-1}{2(x+1)}$
