So I want to find the power series representation of the function $f(x) = \frac{1+x^2}{1-x^2}. $ So how do I solve this?
I can start by reducing the function to the known form of geometric series but I have a summation at the numerator. How do I overcome that?

$\frac{1+x^2}{1-x^2} = \frac{(1+x)^2 -2x}{1-x^2} = \frac{1+x}{1-x} - \frac{2x }{1-x^2}$, now second part I can solve, it would be $2x \sum\_{n =0}^{\infty} x^{2n}.$ How do I go about the first part? Please give some hint. Thank You.