Help with using the quotient rule on a derivative?

I don't know why, but for some reason I absolutely cannot get the answer to this derivative:

h(x) = sqrt(x)/x^3+1

I got as far as writing everything out and trying to simplify it:

(1/2x^-1/2)(x^3+1)-(x^1/2)(3x^2)/(x^3+1)^2

Simplifying:

(1/2)x^-3/2+(1/2)x^-(1/2)-3x/x^3+1

Somehow, I'm supposed to make this equal

1-5x^3/2sqrt(x)(x^3+1)^2

I think I might be making a simple algebra mistake, but I can't find it, so if someone could show me the process to get to the answer, that would help immensely :)