Consider a linear time-invariant system with input x[n] and output y[n] for which 

y[n – 1] – 5/2 y[n] + y[n + 1] = x[n].

The system may or may not be stable or causal. By considering the pole-zero pattern associated with the preceding difference equation, determine three possible choice for the impulse response of the system. Show that each choice satisfies the difference equation. Indicate which choice corresponds to a stable system and which choice corresponds to a causal system.