Answer
$$x=-3,\:x=2$$
Work Step by Step
Solving the equation by isolating the variable using the rules of Algebra, we find:
$$ \frac{2x}{x-1}\left(x-1\right)\left(x-3\right)+\frac{x}{x-3}\left(x-1\right)\left(x-3\right)=2\left(x-1\right)\left(x-3\right)\\ 2x\left(x-3\right)+x\left(x-1\right)=2\left(x-1\right)\left(x-3\right)\\ x=-3,\:x=2$$
