Analyzing Singularities at z=2 & -1/3

[AlBell]

Homework Statement

I have been asked to state the precise nature of the singularities at z=2 and z=-1/3 in

Homework Equations

I know the laurent series is given by

The Attempt at a Solution

I think I need to expand the series out into a laurent series around z=2 and z=-1/3 but I am really stuck on how to do this and would really appreciate a bit of help! From some examples I have seen I need to manipulate the denominator into a known series and then expand this but I am unsure of how to do that. Thanks

 

[Dick]

You don't need to expand anything. You just need to review the definition of a pole of order n.

 

[AlBell]

I know I don't have to but I thought that a laurent expansion was another way to find out the nature of a singularity, like what the order of the pole was, and I just wanted to try and get a grasp of this technique as well and get the same answer for both techniques