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Find the singular part for the function z^2+1/z(z-1)

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The following function f has an isolated singularity at z=0. Its nature: it is a pole; find the singular part.

f(z)=(z^2+1)/(z(z-1))

Use this equation and definition:
Equation: f(z)= A_m/(z-a)^m +⋯+ A_1/((z-a) )+g_1 (z) (*)
Where g_1 is analytic in B(a;R) and A_m≠0.
Definition: if f has a pole of order m at z=0 and satisfies (*) then A_m (z-a)^(-m)+⋯+A_1 (z-a)^(-1) is called the singular part of f at z-a.

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The expert finds the singular part for a function.

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