A. Show that the system of rational expressions is closed under addition, or give an example showing the contrary.

A "rational expression" is a fraction in which the numerator and the denominator are both polynomials. The sum of two such expressions will always produce another such expression, viz.,

p (x) / q (x) + r (x) / s (x) = [p (x) s (x) + q (x) r (x) ] / [q (x) * s (x) ].

The numerator and denominator of the sum will both be polynomials when fully expanded