Đáp án:
Giải thích các bước giải:
$A=(\dfrac{2}{x-1}+\dfrac{3}{x+1}-\dfrac{2x+2}{x^{2}-1}).\dfrac{x^{3}+x}{3x+9}$
$ $
$=\dfrac{2.(x+1)}{(x-1).(x+1)}+\dfrac{3.(x-1)}{(x-1).(x+1)}-\dfrac{2x+2}{(x+1).(x-1)}).\dfrac{x.(x^{2}+1)}{3.(x+3)}$
$ $
$=\dfrac{2x+2+3x-3-2x-2}{(x+1).(x-1)}.\dfrac{x.(x^{2}+1}{3.(x+3)}$
$ $
$=\dfrac{3.(x-1)}{(x+1).(x-1)}.\dfrac{x.(x^{2}+1)}{3.(x+3)}$
$ $
$=\dfrac{x.(x^{2}+1}{(x+1).(x+3)}$
$ $
$=\dfrac{x^{3}+x}{x^{2}+4x+3}$
