I know how to do normal binomial expansions but I can't remember questions quite like this which I've just found in my textbook, by exam being in just over a day.
The first bit is to show that (1+x)/(2+x) - (1-x)/(2-x) = 2x/(4-x^2). I did that fine. The second bit says 'Hence or otherwise show that for small x f(x) = 1/2x + 1/8x^3 + 1/32x^5 and I'm stuck. Any help would be much appreciated.