NOTE: In this description, R represents the symbol for the set of real numbers. I couldn't find a way to type or copy the correct R symbol for the set of real numbers. Also, the parentheses in R(x) is used to distinguish the ring R(x) of rational functions from the ring R[x] of polynomials.
Show that the set R(x) of rational functions p(x)/q(x), where p(x), q(x) are in R[x] and q(x) <> 0, is a field.
It is shown that a set of real rational functions is a field. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.