I'm trying to simplify the following expression
(b (1 - x)^n (-1 + x)^-n (-1 + x - w x)^n)/(n (-1 + w) (1 - x + w x)).
All parameters and the variable x should be positive real numbers. As far as I can see, this can't be simplified further with Simplify or FullSimplify. I know that the simplified expression is
(b*(1 + (-1 + w)*x)^(-1 + n))/(n*(-1 + w))
but I'd like to know how to 'automate' this kind of simplification with Mathematica's functions, if possible.