Curriculum  /  Math  /  11th Grade  /  Unit 4: Rational and Radical Functions  /  Lesson 6

Rational and Radical Functions

Lesson 6

Math

Unit 4

11th Grade

Lesson 6 of 18

Objective

Multiply and divide rational expressions and simplify using equivalent expressions.

Common Core Standards

Core Standards

  • A.APR.D.6 — Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
  • A.APR.D.7 — Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Foundational Standards

  • A.APR.A.1

Criteria for Success

  1. Describe how multiplying or dividing rational expressions is similar to multiplying or dividing numeric fractions. 
  2. Use factoring to identify common factors and simplify the expression. 
  3. Identify domain restrictions on rational expressions. 
  4. Define the vertical and/or horizontal asymptotes graphically by inspection. Compare to the algebraic representation. 

Tips for Teachers

  • Students will likely need to review exponent rules in conjunction with rational exponents. They have not worked extensively with this concept since Algebra 1.
  • Simplifying with rational functions is a tricky concept. Students will need to understand that the best way to simplify a rational expression is to factor the expression first in order to see pairs of factors that simplify to 1. Students will also need to keep track of the factors that are cancelled; the concept of removable discontinuities will be discussed in Lesson 6. 
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Anchor Problems

25-30 minutes

Problem 1

Simplify the rational expression shown below. 

$${x^2+2x-3\over2x^2+2x-12}$$

Guiding Questions

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Problem 2

Find the quotient of the following rational expression: 

$${x^2+3x-40\over{x^2+2x-35}}$$  $${\div }$$  $${x^2+2x-48\over{x^2+3x-18}}$$

Guiding Questions

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Target Task

5-10 minutes

Problem 1

Find the product and write the solution with the fewest number of factors. Note any domain restrictions in your solution. 

$${x-2\over{x^2+x-2}}$$  $${\cdot}$$  $${x^2-3x+2\over{x+2}}$$

References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 24 — Exit Ticket

Algebra II > Module 1 > Topic C > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Find the quotient and write the solution with the fewest number of factors. Note any domain restrictions in your solution. 

$${\left (x-2\over{x^2+x-2}\right )\over\left(x^2-3x+2\over{x+2}\right)}$$

References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 24 — Exit Ticket

Algebra II > Module 1 > Topic C > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Mix these problems from Kuta Software-Infinite Algebra 2 into the problem set.
  • Include problems about domain restrictions as well as radicals and rational exponents to provide consistent review throughout the unit. 
  • Include problems where students start with the vertical asymptotes and other values that are not in the domain, and they create an operation with rational expressions problem. 

Next

Add and subtract rational expressions.

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to Rational and Radical Functions and Expressions

Topic B: Features of Rational Functions and Graphing Rational Functions

Topic C: Solve Rational and Radical Equations and Model with Rational Functions

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