Expand (1+2x)−2(1+2x)^{-2}(1+2x)−2 in ascending powers of x x\,x up to and including x3x^3x3
Write down the range of values of x x\,x for which the expansion is valid.
Use your expansion to find the expansion of 1−x(1+2x)2\displaystyle \frac{1-x}{(1+2x)^2}(1+2x)21−x up to and including x3x^3x3