Must the difference between 2 rational numbers be a rational number?

A/b - c/d with a,b,c,d as integers and b,d ≠ 0. a/b - c/d -> ad/bd - bc/bd --> (ad - bc)/bd
The difference will always be rational. This is because the denominator will never be 0. Everything is closed under some kind of operation, and the answers will always be able to be written as a ratio.
Hope that helped.