$\frac{1}{x}+\frac{1}{x-2}\ge \frac{2}{x^2-2x}$

$\frac{1}{x}+\frac{1}{x-2}-\frac{2}{x^2-2x}\ge 0\Rightarrow \frac{x-2+x-2}{x\left(x-2\right)}\ge 0\Rightarrow \frac{2\left(x-2\right)}{x\left(x-2\right)}\ge 0\Rightarrow \frac{2}{x}\ge 0\Rightarrow x\in ]0,+\infty [$