I have the following question : Find a Laurent expansion of $f(z) = \dfrac{z}{(z^2 + 1)}$, valid for $|z-3| > 2$.
I have learnt finding the Laurent expansion of functions where the denominator is of the form $(z+a)^n$, but this form in the given question seems to be unfamiliar to me. I guess I need to transform it to the $(z+a)^n$ form, but how do I utilise the condition given (that it is valid for $|z-3| > 2$) ?
Thanks in advance.