For the first parts of the question I had to expand $\displaystyle (1+8x)^\frac{1}{2} = 1+4x-8x^2$ and $\displaystyle (1-4x)^\frac{1}{2} = 1+2x+6x^2 $

The next part is to find $\displaystyle \sqrt{(1+8x)/(1-4x)}$

I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...