f(a,b) = b/a = 0 + 0 + b/a = f(a) + f(b) + interaction term

In this case the system is contained entirely within the interaction term, and since you don't know the distributions of a and b there's not much motivation to go further. If you had the distributions of a and b you might be able to do something a little less trivial by skewing the interaction term to have an expected value of zero, potentially like:

a/b = a + b + (a/b - a - b) = f(a) + f(b) + (interaction term with E[term] = 0)

If by "interaction term" it is meant f(a,b), then I congratulate the author of that tautology.

Hidden in the parent's comment is the additional condition that f(a,b) have an expected value of zero. It's still pretty easy to prove, though.