Question

tìm đkxđ và rút gọn

Answer 1

ĐKXĐ: x<>0; x<>2; x<>1; x<>-1

\(Q=1+\dfrac{x+1+x+1-2x^2+2x-2}{\left(x+1\right)\left(x^2-x+1\right)}\cdot\dfrac{x\left(x^2-x-1\right)}{x^2\left(x-2\right)}\)

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

\(=1+\dfrac{-2x\left(x-2\right)}{x\left(x+1\right)\left(x-2\right)}=1+\dfrac{-2}{x+1}=\dfrac{x+1-2}{x+1}=\dfrac{x-1}{x+1}\)