Solve for $x,$ where
\[\frac{x}{x - a} + \frac{x - b}{x - a - b} = \frac{x - a}{x - 2a} + \frac{x + a - b}{x - b}.\]Assume that $2a > x > b > a > 0.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve for $x,$ where
\[\frac{x}{x - a} + \frac{x - b}{x - a - b} = \frac{x - a}{x - 2a} + \frac{x + a - b}{x - b}.\]Assume that $2a > x > b > a > 0.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{2a + b}{2}
Solve for $x,$ where
\[\frac{x}{x - a} + \frac{x - b}{x - a - b} = \frac{x - a}{x - 2a} + \frac{x + a - b}{x - b}.\]Assume that $2a > x > b > a > 0.$
train