Rational functions. A rational function is a function which can be expressed as a quotient of polynomials, i.e. a function whose value at a number x is

where polynomials, and g is not the zero polynomial. Thus a rational function is defined only for those numbers x such that In an expression as above, we call numerator of the rational function, and g its denominator. We can then work with rational functions just as we did with rational numbers. In particular, we can put two rational functions over a common (polynomial) denominator, and take their sum in a manner analogous to taking the sum of rational numbers. We give an example of this.