f(z)= 1/2 x 1/(z-1) - 1/2 x 1/(z-3) = 1/2 x 1/(z-1) - 1/4 x 1/[1-(z-1)/2] = 1/2 x 1/(z-1) - 1/4 x ∑(n=0,∞) [1-(z-1)/2]^n, 0<|(z-1)/2|<1f(z) = 1/2 x 1/(z-1) - 1/4 x ∑(n=0,∞) [1-(z-1)/2]^n, 0<|z-1|<2