Simplifying sqrt(4*z^2-4*z+1)?



Assume |z| <= 1/2, how can I get maxima to simplify

(sqrt(4*z^2-4*z+1)-1)/(2*z^2-2*z)?

ratsimp and factor don't really do anything. radcan does, but the
answer is wrong.

If factor looked inside the sqrt, it would see that 4*z^2-4*z+1 is
(2*z-1)^2.  If we manually do that, maxima notices:

(sqrt((2*z-1)^2)-1)/(2*z^2-2*z) -> -1/(z-1)

or 1/(1-z), which is what I wanted.

Ray