$\frac{2}{x+2}+\frac{x}{2-x}=\frac{2}{2-x}-\frac{x}{2+x}$  

$D=\mathbb{R}\backslash \left\{-2;2\right\}$  

  

$\frac{2}{x+2}+\frac{x}{2-x}=\frac{2}{2-x}-\frac{x}{2+x}$  

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

 

$2\left(2-x\right)+x\left(x+2\right)=2\left(2+x\right)-x\left(2-x\right)$  

$4-2x+x^2+2x=4+2x-2x+x^2$  

$0=0$  

$x\in D$  

$\underline{x\in \mathbb{R}\backslash \left\{-2;2\right\}}$