I am working on a problem, the remaining step I need to do is very computational.

I am mathematically software challenged, can some one find the solution to this problem:

Find $\displaystyle a,b,c,d,e,f,g,h$ (real numbers) and with $\displaystyle a,e\not = 0$ so that if in the function $\displaystyle f(x) = \tfrac{ax^3+bx^2+cx+d}{ex^3+fx^2+gx+h}$ we replace $\displaystyle x$ by $\displaystyle \tfrac{ - x - \sqrt{3}}{\sqrt{3}x-1}$ then we end up with the same function, i.e. $\displaystyle f(x) = f\left( \tfrac{-x-\sqrt{3}}{\sqrt{3}x-1} \right)$.