Finding the intervals of increase and decrease of $\frac{x^4 - x^3 -8}{x^2 - x - 6}$ How can I find the intervals of increase and decrease of $\frac{x^4 - x^3 -8}{x^2 - x - 6}$?
I tried to find the derivative by the quotient rule to obtain the critical points but the formula was getting complicated, I know that $D_f = \mathbb{R} \setminus \{-2,3\}$  but then what?
Could anyone help me please?

The sign of the derivative of $\frac{x^4 - x^3 -8}{x^2 - x - 6}$ is exactly the same sign of $-4+8x+9x^2-11x^3-2x^4+x^5$. This polynomial has no rational roots:

