Sau khi rút gọn biểu thức \(\dfrac{2x^2+x+5}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac{2}{x+1}\), ta có kết quả là
\(\dfrac{x+2}{x^2-x+1}\).\(\dfrac{2}{x+1}\).\(\dfrac{x-2}{x^2+x+1}\).\(\dfrac{x+1}{x^2+x+1}\).Hướng dẫn giải:\(\dfrac{2x^2+x+5}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac{2}{x+1}\)
\(=\dfrac{2x^2+x+5+\left(x-1\right)\left(x+1\right)-2\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{2x^2+x+5+x^2-1-2x^2+2x-2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x^2+3x+2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x+2}{x^2-x+1}\).