Expand (1+4x)−2(1+4x)^{-2}(1+4x)−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 3x−1(1+4x)2\displaystyle \frac{3x-1}{(1+4x)^2}(1+4x)23x−1 up to and including x3x^3x3