Question

tính phân thức:1/x-1-2/x+1+1/x+2

  

Answer 1

  

Answer 2

\(\dfrac{1}{x-1}-\dfrac{2}{x+1}+\dfrac{1}{x+2}\) (ĐK: \(x\ne-2;x\ne\pm1\))

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

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

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

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

\(=\dfrac{3x+6-x^2-2x+x^2-1}{\left(x+1\right)\left(x-1\right)\left(x+2\right)}\)

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