Khi thực hiện phép tính \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\), ta có kết quả là
\(\dfrac{1}{x+1}\).\(\dfrac{x}{x+1}\).\(\dfrac{x-1}{x+1}\).\(\dfrac{x-1}{x+1}\).Hướng dẫn giải:\(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left[\dfrac{1}{x\left(x+1\right)}-\dfrac{2-x}{x+1}\right]:\dfrac{1+x^2-2x}{x}\)
\(=\dfrac{1-x\left(2-x\right)}{x\left(x+1\right)}.\dfrac{x}{x^2-2x+1}\)
\(=\dfrac{x^2-2x+1}{x\left(x+1\right)}.\dfrac{x}{x^2-2x+1}\)
\(=\dfrac{1}{x+1}\).
