I was not really prepared to answer, but given that you asked in an A2A, and given that the answers so far did not understand the question, I will try.
First, the definition is needed. A function f is rational if and only if it is the quotient of two polynomials… that is, expressible in the form
f(x) = P(x) / Q(x) where P and Q are polynomials.
In particular, if P and Q have degree 1, then f(x) = (ax + b) / (cx + d)
where a, b, c, and d are constants. My first examples will both use this.
A specific example would be f(x) = x / (x + 1).
Customarily, the ratio should be in lowest terms, such as
(x + 2) / x but NOT (3x + 6) / 3x (because of common factor 3).
