CHAPTER 4 - RATIONAL FUNCTIONS

Abstract

This chapter focuses on rational functions. A rational function r(x) is the quotient of two polynomials. A rational function can be written as a quotient of polynomials in many ways. Each rational number and each rational function possess expressions in lowest terms. Rational functions are added by writing them with a common denominator and then adding their numerators. The result of each algebraic operation on a pair of rational functions is a rational function. The collection of rational functions is closed under the operations of addition, subtraction, multiplication, and division by a nonzero rational function. There is an analogous reduction for a rational function if the degree of its numerator is greater than or equal to the degree of its denominator. By long division, any rational function can be reduced to the sum of a polynomial and a bottom-heavy rational function.