Khi thực hiện các phép tính \(\dfrac{2x+1}{\left(x+1\right)^2}-\dfrac{1}{x-1}+\dfrac{x+2}{x^2-1}\), ta có kết quả là
\(\dfrac{2x^2}{\left(x+1\right)^2\left(x-1\right)}\).\(\dfrac{1}{x-1}\).\(\dfrac{4x^2+4x+2}{\left(x+1\right)^2\left(x-1\right)}\).\(\dfrac{x^2+x+1}{\left(x+1\right)^2\left(x-1\right)}\).Hướng dẫn giải:\(\dfrac{2x+1}{\left(x+1\right)^2}-\dfrac{1}{x-1}+\dfrac{x+2}{x^2-1}\)
\(=\dfrac{2x+1}{\left(x+1\right)^2}-\dfrac{1}{x-1}+\dfrac{x+2}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\left(x-1\right)\left(2x+1\right)-\left(x+1\right)^2+\left(x+2\right)\left(x+1\right)}{\left(x+1\right)^2\left(x-1\right)}\)
\(=\dfrac{2x^2-x-1-x^2-2x-1+x^2+3x+2}{\left(x+1\right)^2\left(x-1\right)}\)
\(=\dfrac{2x^2}{\left(x+1\right)^2\left(x-1\right)}\).