problem says :

function develop in too Laurent series in region

i really don't have much trouble with series but (perhaps this is more thread for Pre-university math ) i have problem with this one, especially how to do partial fraction of this function ...

i have perhaps 10 - 15 pages of the work and jet i didn't get the correct answer i'll post here some of the work where I think that if i do this correctly i solve rest myself

because up (can't be sure how to say it on English ) in fraction have bigger power than down to use partial fractions i need to divide it first so sown should have "z" with higher power (or am I mistaking ? because if not than i really don't know how to do it)

when dividing with i get

and now i do partial fractions :

am I on the good path so far ? if not how can i solve this (even if I am on the good path, is there some more simple way to do this ? )

sorry if this is wrong sub forum for this type of the question

thanks in advance