I'm trying to solve a recurrence relation using generating function and I reached the following point in the solution:
$$\phi(t)=(24t^2-54t)/(-20t^3+24t^2-9t)$$
How could I continue from here? I know I'm supposed to get 3 constants as a result and then use them with the recurrence relation in order to solve it but I'm stuck on this damned fraction.