ĐKXĐ: \(x\ne\left\{0;-2\right\}\)
\(\dfrac{x-2}{x^2+2x}-\dfrac{x}{2x+4}=\dfrac{x-2}{x\left(x+2\right)}-\dfrac{x}{2\left(x+2\right)}\)
\(=\dfrac{2\left(x-2\right)}{2x\left(x+2\right)}-\dfrac{x^2}{2x\left(x+2\right)}=\dfrac{-x^2+2x-4}{2x\left(x+2\right)}\)