Divide and Conquer: Mastering Rational Expressions

Algebra 2 Grades High School 7:19 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to divide rational expressions, identify excluded values, and simplify the results. This lesson reinforces factoring skills and builds a strong foundation for advanced algebraic concepts.

Video Resource

Dividing Rational Expressions and Identifying Excluded Values

Mario's Math Tutoring

Duration: 7:19
Watch on YouTube

Key Concepts

  • Rational Expressions
  • Excluded Values (Division by Zero)
  • Reciprocal
  • Factoring
  • Simplifying Rational Expressions

Learning Objectives

  • Students will be able to divide rational expressions by multiplying by the reciprocal.
  • Students will be able to identify excluded values of rational expressions.
  • Students will be able to simplify rational expressions by factoring and canceling common factors.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of dividing fractions and how it relates to multiplying by the reciprocal. Briefly discuss why division by zero is undefined and its implications for rational expressions.
  • Video Instruction (15 mins)
    Watch the "Dividing Rational Expressions and Identifying Excluded Values" video by Mario's Math Tutoring. Encourage students to pause the video at the example problems and attempt to solve them independently before watching the solution.
  • Guided Practice (15 mins)
    Work through additional examples of dividing rational expressions as a class. Emphasize the importance of factoring completely and identifying all excluded values (including those from the numerator of the divisor). Break down each step and answer student questions.
  • Independent Practice (10 mins)
    Assign students practice problems to work on individually. Circulate to provide support and answer questions. Collect the completed problems for assessment.
  • Wrap-up (5 mins)
    Summarize the key steps for dividing rational expressions and identifying excluded values. Preview the upcoming lesson and assign homework.

Interactive Exercises

  • Error Analysis
    Present students with incorrectly solved problems and ask them to identify the errors in the factoring, simplification, or identification of excluded values. Discuss the correct approach.
  • Rational Expression Matching
    Create pairs of equivalent rational expressions (one simplified, one not). Have students match the pairs by factoring and simplifying.

Discussion Questions

  • Why is it important to factor rational expressions before simplifying?
  • How do you identify excluded values in a rational expression, and why are they important?
  • Explain the process of dividing rational expressions. What does 'keep it, change it, flip it' mean in this context?
  • Why do you need to consider the numerator of the divisor when determining excluded values?

Skills Developed

  • Factoring Polynomials
  • Simplifying Algebraic Expressions
  • Identifying Restrictions on Variables
  • Applying the Reciprocal in Division
  • Problem-Solving

Multiple Choice Questions

Question 1:

When dividing rational expressions, which of the following is the correct first step after factoring?

Correct Answer: Multiply by the reciprocal of the second expression

Question 2:

What are excluded values in a rational expression?

Correct Answer: Values that make the denominator zero

Question 3:

Which of the following is equivalent to (x+2)/(x-3) divided by (x+2)/(x+5)?

Correct Answer: (x+5)/(x-3)

Question 4:

When identifying excluded values for division of rational expressions, you must consider the denominator of the original expression AND:

Correct Answer: The numerator of the expression you are dividing by

Question 5:

Simplify: (x^2 - 4) / (x+2)

Correct Answer: x - 2

Question 6:

What is the excluded value for the expression 1/(x-5)?

Correct Answer: 5

Question 7:

Which factoring method is commonly used when simplifying rational expressions?

Correct Answer: Difference of Squares

Question 8:

When can you cancel terms in a rational expression?

Correct Answer: When the terms are multiplied

Question 9:

Dividing by a rational expression is the same as multiplying by its ___________.

Correct Answer: Reciprocal

Question 10:

What is the simplified form of (x+1)(x-1) / (x+1)?

Correct Answer: x-1

Fill in the Blank Questions

Question 1:

When dividing rational expressions, you multiply by the ___________ of the second expression.

Correct Answer: reciprocal

Question 2:

Values that make the denominator of a rational expression equal to zero are called ___________ ___________.

Correct Answer: excluded values

Question 3:

Before simplifying rational expressions, it's essential to ___________ the numerator and denominator.

Correct Answer: factor

Question 4:

The phrase "keep it, change it, flip it" refers to dividing ___________.

Correct Answer: fractions

Question 5:

x cannot be equal to _______ in the expression 1/(x+3)

Correct Answer: -3

Question 6:

When simplifying, factors that are common to both the numerator and denominator can be __________.

Correct Answer: cancelled

Question 7:

If a rational expression simplifies to 1, it means the original numerator and denominator were __________.

Correct Answer: equal

Question 8:

The first step in simplifying any rational expression is to completely ___________ the numerator and denominator.

Correct Answer: factor

Question 9:

The numerator of the second fraction must also be considered when determining ____________ values.

Correct Answer: excluded

Question 10:

Dividing by a fraction is equivalent to multiplying by its ____________.

Correct Answer: reciprocal

Educational Standards

A2.A.2.3:Add, subtract, multiply, divide, and simplify rational expressions. A2.A.1.3:Solve one-variable rational equations and check for extraneous solutions. A2.A.2.1:Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans