Yes, it is. The set of rational numbers is closed for all the four operations, so x+y, x-y, x*y and x/y are rational too. And it is easy to demonstrate. A rational number can be expressed as a fraction of two integers. So, x can be expressed as a/b and y as c/d. Hence x+y = a/b + c/d = (ad+bc)/bd, which, as fraction of two integers, is rational.
