Sau khi rút gọn biểu thức \(\dfrac{2x^2+4}{x^3+1}+\dfrac{1}{x+1}-\dfrac{2}{x^2-x+1}\), ta có kết quả là
\(\dfrac{x+2}{x^2-x+1}\).\(\dfrac{3}{x+1}\).\(\dfrac{x-2}{x^2-x+1}\).\(\dfrac{x+1}{x^2-x+1}\).Hướng dẫn giải:\(\dfrac{2x^2+4}{x^3+1}+\dfrac{1}{x+1}-\dfrac{2}{x^2-x+1}\)
\(=\dfrac{2x^2+4+x^2-x+1-2\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{2x^2+4+x^2-x+1-2x-2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{3x^2-3x+3}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{3}{x+1}\).