I'm working on an assignment and the probelm asks to differentiate h(x) = (x^1/3)/(x^3+1)

I keep getting (x^3 + 1 - 3x^(7/3)) / (3x^(2/3)(x^3 + 1)^2

However, the answer in the back of the book is: (1 - 8x^3) / (3x^(2/3)(x^3 + 1)^2

I've reworked this problem several times and i cannot figure out what I'm doing wrong. I would appreciate any help. Thanks!