1,
\(\dfrac{1}{x^2+x+1}+\dfrac{1}{x^2-x}+\dfrac{2x}{1-x^3}\\ =\dfrac{1}{x^2+x+1}+\dfrac{1}{x\left(x-1\right)}-\dfrac{2x}{\left(x-1\right)\left(x^2+x+1\right)}\\ =\dfrac{x^2-x}{x\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{x^2+x+1}{x\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{2x^2}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2-x+x^2+x+1-2x^2}{x\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^4-x}\)
2/
\(\dfrac{2x+1}{2x^2-x}+\dfrac{32x^2}{1-4x^2}-\dfrac{1-2x}{2x^2+x}\\ =\dfrac{2x+1}{x\left(2x-1\right)}-\dfrac{32x^2}{\left(2x-1\right)\left(2x+1\right)}-\dfrac{1-2x}{x\left(2x+1\right)}\)
\(=\dfrac{4x^2+4x+1}{x\left(2x-1\right)\left(2x+1\right)}-\dfrac{32x^3}{x\left(2x-1\right)\left(2x+1\right)}-\dfrac{4x^2-4x+1}{x\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{4x^2+4x+1-32x^3-4x^2+4x-1}{x\left(2x-1\right)\left(2x+1\right)}=\dfrac{-32x^3+8x}{x\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{-8x\left(4x^2-1\right)}{x\left(2x-1\right)\left(2x+1\right)}=\dfrac{-8x\left(2x-1\right)\left(2x+1\right)}{x\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{-8x}{x}=-8\)
