Question

Tính:    \(\frac{1-5x-4x^2}{x^3+2x^2-x-2}-\frac{3x+1}{2-x-x^2}\)

Answer 1

\(=\dfrac{-4x^2-5x+1}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}+\dfrac{3x+1}{\left(x+2\right)\left(x-1\right)}\)

\(=\dfrac{-4x^2-5x+1+3x^2+4x+1}{\left(x+2\right)\left(x-1\right)\left(x+1\right)}\)

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

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