\(Q=\left(\dfrac{2x-x^2}{2x^2}+\dfrac{8-2x^2}{\left(x-2\right)\left(x^2+4\right)}\right)\cdot\left(\dfrac{2}{x^2}+\dfrac{1-x}{x}\right)\)
\(=\left(\dfrac{2-x}{2x}-\dfrac{2\left(x+2\right)}{x^2+4}\right)\cdot\dfrac{2+x-x^2}{x^2}\)
\(=\dfrac{2x^2+8-x^3-4x-4x\left(x+2\right)}{2x\left(x^2+4\right)}\cdot\dfrac{-\left(x-2\right)\left(x+1\right)}{x^2}\)
\(=\dfrac{2x^2+8-x^3-4x-4x^2-8x}{2x\left(x^2+4\right)}\cdot\dfrac{-\left(x-2\right)\left(x+1\right)}{x^2}\)
\(=\dfrac{-x^3-2x^2-12x+8}{2x\left(x^2+4\right)}\cdot\dfrac{-\left(x-2\right)\left(x+1\right)}{x^2}\)
\(=\dfrac{\left(x^3+2x^2+12x-8\right)\left(x-2\right)\left(x+1\right)}{2x^3\left(x^2+4\right)}\)
