1. The problem statement, all variables and given/known data 2. Relevant equations H(z) = Y(z)/X(z) 3. The attempt at a solution I realized this wasn't in partial fraction form because the 1+z-1+0.5z-2 has non-real roots. I multiplied the 1st fraction part by z1 and the 2nd fraction by z2, then I combined them into one fraction and I think I am able to get a difference equation at the end, but is the way I am doing it right? Or is there an easier way to do this problem that I am missing.