`x/(x-2)+(x+2)/x>2`
`<=>(x^2+x^2-4-2(x^2-4))/(x(x-2))>0`
`<=>4/(x(x-2))>0`
`<=>x(x-2)>0``
`<=>` $\left[ \begin{array}{l}\begin{cases}x>0\\x>2\end{cases}\\\begin{cases}x<0\\x<2\end{cases}\end{array} \right.$
`<=>` $\left[ \begin{array}{l}x>2\\x<0\end{array} \right.$