\(=\frac{x+2}{2-x}.\frac{\left(x-2\right)^2}{4x^2}.\left[\frac{2}{1-x}-\frac{4}{\left(x+2\right)\left(x-2\right)}\right]\)

\(=\frac{-\left(x+2\right)}{x-2}.\frac{\left(x-2\right)^2}{4x^2}.\frac{-2x}{x^2-4}\)

\(=\frac{x+2}{2x}\)