Rút gọn các biểu thức sau: d) 1+ x^3-x/ x^2+1( 1/ 1-x- 1/ 1-x^2).

Trả lời

d, $1+\frac{x^3-x}{x^2+1}\left(\frac{1}{1-x}-\frac{1}{1-x^2}\right)=1+\frac{x(x^2-1)}{x^2+1}.\left(\frac{1}{1-x}-\frac{1}{1-x^2}\right)$

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

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

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

$=\frac{1}{x^2+1}$