I have this problem requiring me to show two infinite sums are equal but I can't seem to figure out how to do this. No matter what I try never give any results.

Hence my question is what approach should I use toward one of these question?

This is the question in question if it can help

Show

$\displaystyle

\sum_{p=0}^{\infty}\frac{x^{2p}}{1+x^{4p+2}}=\sum_ {q=0}^{\infty} (-1)^{q}\frac{x^{2q}}{1-x^{4q+2}}

$

if |x|<1