sage: var('U,z');
sage: V = 1/U
sage: EE = (z^2-1)^2 / z^2 / (z-U) / (z-V)
sage: EE.partial_fraction(z)
-(U^2 - 1)/(U*z - 1) - (U^2 - 1)/((U - z)*U) + (U^2 + 1)/(U*z) + 1/z^2 + 1
sage: bool( _ == (1 + 1/z^2 + (U+V)/z - (V-U)/(z-U) - (U-V)/(z-V) ) )
True