Answer
$$x=5,\:x=\frac{1}{2}$$
Work Step by Step
We solve the equation using cross multiplication. Doing this, we find:
$$\frac{x-3}{x+2}=\frac{x-1}{3x-1} \\ \left(x-3\right)\left(3x-1\right)=\left(x+2\right)\left(x-1\right) \\ x=5,\:x=\frac{1}{2}$$
Checking, we see that the solution is not extraneous.
