Prove the following statement directly from the definition

Last updated: 7/9/2022

Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = a/b and s = c/d for some a, b, c, and d with Write r - s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. Both the numerator and the denominator are integers because In addition, bd ≠ 0 by the Hence r-s is a of two integers with a nonzero denominator, and so by definition of rational, r- s is rational.