Download presentation

Presentation is loading. Please wait.

Published byCalvin Richard Modified over 4 years ago

2
Chapter 6 Section 1

3
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 1 The Fundamental Property of Rational Expressions Find the numerical value of a rational expression. Find the values of the variable for which a rational expression is undefined. Write rational expressions in lowest terms. Recognize equivalent forms of rational expressions. 6.1 2 3 4

4
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Rational Expressions Examples of rational expressions: Rational expressions cannot have a denominator equal to 0 Slide 6.1-3

5
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Find the numerical value of a rational expression. Slide 6.1-4

6
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find the value of the rational expression, when x = 3. Solution: Slide 6.1-5 Evaluating Rational Expressions CLASSROOM EXAMPLE 1

7
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Find the values of the variable for which a rational expression is undefined. Slide 6.1-6

8
Copyright © 2012, 2008, 2004 Pearson Education, Inc. The 11 th Commandment Thou shall not… divide by zero The denominator of a rational expression cannot equal 0 because Division by 0 is Undefined For instance, in the rational expression If x is 2, then the denominator becomes 0, making the expression undefined. Thus, x cannot equal 2. We indicate this restriction by writing x ≠ 2. Denominator cannot equal 0 Slide 6.1-7

9
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Finding Restrictions on the Variable Step 1: Set the denominator of the rational expression equal to 0. Step 2: Solve this equation. Step 3: The solutions of the equation are the values that make the rational expression undefined. The variable cannot equal these values. Slide 6.1-8 Determining When a Rational Expression is Undefined

10
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find any values of the variable for which each rational expression is undefined. Solution: never undefined Slide 6.1-9 Finding Values That Make Rational Expressions Undefined CLASSROOM EXAMPLE 2

11
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Write rational expressions in lowest terms. Slide 6.1-10

12
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Write rational expressions in lowest terms. Fundamental Property of Rational Expressions where K ≠ 0 and Q ≠ 0 Lowest Terms If the greatest common factor of its numerator and denominator is 1. This property is based on the identity property of multiplication, since Slide 6.1-11

13
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Write each rational expression in lowest terms. Slide 6.1-12 Writing in Lowest Terms CLASSROOM EXAMPLE 3

14
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Only common factors can be divided out, not common addends!!! Step 1: Factor the numerator and denominator completely. Step 2: Use the fundamental property to divide out any common factors. Addends cannot be divided out. Slide 6.1-13 Writing a Rational Expression in Lowest Terms Like This NOT like this!

15
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Write in lowest terms. Slide 6.1-14 Writing in Lowest Terms CLASSROOM EXAMPLE 4

16
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Quotient of Opposites If the numerator and the denominator of a rational expression are opposites, as in then the rational expression is equal to −1. Write in lowest terms. Slide 6.1-15 Writing in Lowest Terms (Factors Are Opposites) CLASSROOM EXAMPLE 5

17
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Write each rational expression in lowest terms. or Slide 6.1-16 Writing in Lowest Terms (Factors Are Opposites) Solution: CLASSROOM EXAMPLE 6

18
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 4 Recognize equivalent forms of rational expressions. Slide 6.1-17

19
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Recognize equivalent forms of rational expressions Three ways to write the common fraction = = The − sign representing the factor −1 is in front of the expression. = = The factor may instead be placed in the numerator or in the denominator. Slide 6.1-18

20
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Be careful to apply the distributive property correctly. Choose the equivalent expression. Explain. a. b. Slide 6.1-19 Recognize equivalent forms of rational expressions

21
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Write four equivalent forms of the rational expression. Solution: Slide 6.1-20 Writing Equivalent Forms of a Rational Expression CLASSROOM EXAMPLE 7

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google