I have to determine if $$(1 - 1.1B + 0.8B^2)Y_t = (1 - 1.7B + 0.72B^2)a_t$$

is stationary, invertible or both.

I have shown that $\Phi(B) = 1 - 1.1B + 0.8B^2 = 0$ when $B_{1,2} = 0.6875 \pm 0.8817i$, whose moduli are both larger than 1, hence is stationary. Similarly, I have shown that $\Theta(B) = 1 - 1.7B + 0.72B^2 = 0$, when $B_1 = 1.25 > 1$ and $B_2 = 1.11 > 1$, hence is invertible.

I also need to express the model as a MA and AR representation if it exists; which they do as I have already shown. However, to write as an MA process, I would need to write as: $$Y_t = \frac{1 - 1.7B + 0.72B^2}{1 - 1.1B + 0.8B^2}a_t$$

and for an AR process as: $$\frac{1 - 1.1B + 0.8B^2}{1 - 1.7B + 0.72B^2}Y_t = a_t$$

However, I am confused on how to do this given the division of the quadratic expressions. Should I use long division or is there some expansion formula I should be using?