The problem:

If $\displaystyle a$ and $\displaystyle b$ are positive numbers, prove that the equation

$\displaystyle \frac{a}{x^3+2x-1}+\frac{b}{x^3+x-2}=0$

has at least one solution in the interval (-1,1).

I was hoping for some pointers on how to proceed.

Sorry, I made a mistake earlier that $\displaystyle 2x$ was supposed to be a $\displaystyle 2x^2$.