You have not given me enough information to answer that question. I need to know the context. Are we talking about a ring, a sphere, the real number line, some other context?

Would it suffice to say:

a/b = ab^{+} where b^{+} is a generated inverse of b, and a = 3, b = 0, which is to say:

3/0 = 3*0^{+}

The point being, division by zero is an issue with the context of real number lines, not an issue with math in general. Its a rule made for conveinence, but as with all other rules it is prudent to break them for examination. Math isn't a set of rules to follow, its a set of rules to use and abuse.