Sửa đề:
\(Q=1+\left(\dfrac{x+1}{x^3+1}-\dfrac{1}{x^2-x+1}-\dfrac{2}{x+1}\right):\dfrac{x^3-2x^2}{x^3-x^2+x}\)
\(=1+\left(\dfrac{x+1}{\left(x+1\right)\left(x^2-x+1\right)}-\dfrac{x+1}{\left(x+1\right)\left(x^2-x+1\right)}-\dfrac{2\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\right):\dfrac{x^2\left(x-2\right)}{x\left(x^2-x+1\right)}\)
\(=1+\dfrac{x+1-x-1-2x^2+2x-2}{\left(x+1\right)\left(x^2-x+1\right)}:\dfrac{x^2\left(x-2\right)}{x\left(x^2-x+1\right)}\)
\(=1+\dfrac{-2x^2+2x-2}{\left(x+1\right)\left(x^2-x+1\right)}:\dfrac{x\left(x-2\right)}{x^2-x+1}\)
\(=1+\dfrac{-2\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\cdot\dfrac{x^2-x+1}{x\left(x-2\right)}\)
\(=1+\dfrac{-2\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-2x\right)}=\dfrac{\left(x+1\right)\left(x^2-2x\right)-2\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-2x\right)}\)
\(=\dfrac{x^3-2x^2+x^2-2x-2x^2+2x-2}{\left(x+1\right)\left(x^2-2x\right)}\)
\(=\dfrac{x^3-3x^2-2}{\left(x+1\right)\left(x^2-2x\right)}\)
