multiply and simplify
z^2-7z-18/z^2-4z+4*z-2/z-9
z^2-7z-18 = (z-9)(z+2)
z^2-4z+4 = (z-2)(z-2)
so,
(z-9)(z+2)/(z-2)(z-2) * (z-2)/(z-9) = (z+2)/(z-2)
z^2-7z-18/z^2-4z+4*z-2/z-9
z^2-4z+4 = (z-2)(z-2)
so,
(z-9)(z+2)/(z-2)(z-2) * (z-2)/(z-9) = (z+2)/(z-2)