constructing a Laurent series

Question

I'm trying to find a Laurent series centered at z=0 for $\dfrac{1}{z^4+z^2}$.

I'm not sure how to approach this. A partial fraction decomposition gives $\dfrac{1}{z^2}-\dfrac{1}{z^2+1}$, but then I am left with the problem of a series for the $z^2+1$ term. Thanks in advance for any suggestions!

Answer 1

You can use the geometric series, to obtain $$ \frac{1}{1+z^2}=\sum_{n=0}^{\infty}(-z^2)^n $$