2.9.1 Functional sequences and series

Problem: Find the sums of the following series: \[ \sum_{n=1}^{\infty} \frac{x^{n+1}}{\left(1-x^{n}\right)\left(1-x^{n+1}\right)} \] if a) \( |x|<1 \); b) \( |x|>1 \).