$$\frac{x}{x-2}<3-\frac{2}{X-2}$$
$\left\{\begin{matrix}x>-\frac{3X-8}{3-X}\text{, }&X>3\text{ or }X<2\\x<2\text{, }&X<2\text{ or }X\geq 3\\x\in \left(-\frac{3X-8}{3-X},2\right)\text{, }&X>2\text{ and }X<3\end{matrix}\right.$
$\left\{\begin{matrix}X>-\frac{8-3x}{x-3}\text{, }&x<0\text{ or }x>3\text{ or }\left(x>0\text{ and }x<2\right)\\X<2\text{, }&x<0\text{ or }\left(x\geq 0\text{ and }x<2\right)\text{ or }x\geq 3\\X\in \left(-\frac{8-3x}{x-3},2\right)\text{, }&x>2\text{ and }x<3\\X>\frac{8}{3}\text{, }&x=0\end{matrix}\right.$