DSP-rational Z- transform?

Question

consider a RATIONAL Z- TRANSFORM

G(Z)= P(Z)/D(Z) where P(Z) and D(z) are polynomials in 1/z.

let Aj denotes the residue of G(z) at a simple pole at Z=Wj.

show that

Aj = - Wj [P(z) / D'(Z)] at Z = Wj

Answer 1

Do you have a value of P(z) and D(z)?

Let's say that:

D(z) = (z-zo)H(z)

Then G(z) = P(z) / D(z) = P(z) / (z-zo)H(z)

with residue Aj = P(zo) / H(zo)

D(z) = (z-zo)H(z) where H(zo) = D'(zo)

showing residue Aj = P(zo) / D'(zo)