jmc

We have the equation $\frac{2x-1}{2x+2}=\frac{x-3}{x-1}$. Cross-multiplying and simplifying, we get $$\begin{array}{rl}(2x-1)(x-1)& =(2x+2)(x-3)\\ 2x^2-x-2x+1& =2x^2+2x-3\cdot 2x-3\cdot 2\\ 2x^2-3x+1& =2x^2-4x-6\\ x& =\boxed{-7}\end{array}$$