If m and n are integers and neither m nor n is zero, is (m + n)/mn a rational number?

Question

I'm not sure whether to prove this by cases or by contradiction. I've tried doing case 1: rational ; case 2: irrational and seem to end up with an irrational number except if both m and n are equal to 2 or 1. How do I go about proving this statement?

Answer 1

What is your definition of rational number? Certainly the numerator and denominator are integers and the denominator is nonzero. For this you just need the closure of the integers under addition and multiplication plus the fact that there are no zero divisors.