ĐKXĐ: x<>1
\(A=\dfrac{x+2}{x^2+x+1}-\dfrac{2}{x-1}-\dfrac{2x^2+4}{1-x^3}\)
\(=\dfrac{x+2}{x^2+x+1}-\dfrac{2}{x-1}+\dfrac{2x^2+4}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)-2\left(x^2+x+1\right)+2x^2+4}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2+x-2-2x^2-2x-2+2x^2+4}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2-x}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x}{x^2+x+1}\)
\(A=\dfrac{x+2}{x^2+x+1}-\dfrac{2}{x-1}-\dfrac{2x^2+4}{1-x^3}\)
ĐKXĐ: \(x\ne1\)
\(A=\dfrac{\left(x+2\right)\left(x-1\right)-2\left(x^2+x+1\right)+\left(2x^2+4\right)}{x^3-1}\)
\(=\dfrac{x^2-x+2x-2-2x^2-2x-2+2x^2+4}{x^3-1}\)
\(=\dfrac{x^2-x}{x^3-1}\)
\(=\dfrac{x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x}{x^2+x+1}\)
