Expand (1+3x)−3(1+3x)^{-3}(1+3x)−3 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 2x+1(1+3x)3\displaystyle \frac{2x+1}{(1+3x)^3}(1+3x)32x+1 up to and including x3x^3x3