Lesson: Multiplying and Dividing Rational Functions Mathematics

In this lesson, we will learn how to multiply and divide rational functions.

Lesson Plan

Objectives

Students will be able to

  • multiply and simplify rational functions, stating the resulting domains,
  • divide and simplify rational functions, stating the resulting domains,
  • simplify expressions involving multiplication and division of rational functions, stating the domains of any resulting function,
  • evaluate the product or quotient of two rational functions.

Prerequisites

Students should already be familiar with

  • functions and their domains,
  • simplifying rational functions.

Exclusions

Students will not cover

  • adding and subtracting rational functions.

Sample Question Videos

  • 04:32
  • 10:11
  • 04:33

Lesson Worksheet

Q1:

Answer the following questions for the rational expressions 5𝑥−45𝑥12𝑥−4𝑥 and 15𝑥−453𝑥.

Evaluate 5𝑥−45𝑥12𝑥−4𝑥 divided by 15𝑥−453𝑥.

Is the result of 5𝑥−45𝑥12𝑥−4𝑥 divided by 15𝑥−453𝑥 a rational expression?

Would this be true for any rational expression divided by another rational expression?

Q2:

Answer the following questions for the rational expressions 6(𝑥−2)3𝑥−6𝑥 and 6𝑥−32𝑥.

Find the product of 6(𝑥−2)3𝑥−6𝑥 and 6𝑥−32𝑥.

Is the product of 6(𝑥−2)3𝑥−6𝑥 and 6𝑥−32𝑥 a rational expression?

Would this be true for the product of any two rational expressions?

Q3:

Simplify the function 𝑛(𝑥)=𝑥+5𝑥+9𝑥+20×𝑥+15𝑥+547𝑥+69𝑥+54, and determine its domain.

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