Let X(z) denote a ratio of polynomials in z; i.e., Show that if X(z) has a 1st-...

Let X(z) denote a ratio of polynomials in z; i.e.,

Show that if X(z) has a 1^st-order pole at z = z₀, then the residue of X(z) at z = z₀ is equal to

where A’(z₀) denotes the derivative of A(z) evaluated at z = z₀.