Answer
$$x=\frac{1}{3}$$
Work Step by Step
In order to solve this equation, we find the common denominator of the two fractions. However, instead of trying to combine the fractions, we multiply both sides of the equation by this denominator. Doing this, we find:
$$\frac{x-4}{x-2}\left(x-2\right)-\frac{2x-1}{x-2}\left(x-2\right)=2\left(x-2\right) \\ x-4-\left(2x-1\right)=2\left(x-2\right) \\ -x-3=2x-4 \\ x=\frac{1}{3}$$
Checking, we see that the solution is not extraneous.
