1. Chapter 7 Section 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. 1 1 2 2 3 3 Adding and Subtracting Rational Expressions Add and subtract rational expressions with the same denominator. Find a least common denominator. Add and subtract rational expressions with different denominators. 7.27.2

3. Slide 7.2- 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 1 Add and subtract rational expressions with the same denominator.

4. Slide 7.2- 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Adding or Subtracting Rational Expressions Step 1If the denominators are the same, add or subtract the numerators. Place the result over the common denominator. If the denominators are different, first find the least common denominator. Write all rational expressions with this least common denominator, and then add or subtract the numerators. Place the result over the common denominator. Step 2Simplify. Write all answers in lowest terms.

5. Slide 7.2- 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Add or subtract as indicated. EXAMPLE 1

6. Slide 7.2- 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 2 Find a least common denominator.

7. Slide 7.2- 7 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Finding the Least Common Denominator Step 1Factor each denominator. Step 2Find the least common denominator. The LCD is the product of all of the different factors from each denominator, with each factor raised to the greatest power that occurs in any denominator.

8. Slide 7.2- 8 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Find the LCD for each group of denominators. a. b. z, z + 6 Factor.10a 3 b 5 = 2 5 a 3 b 5 15a 2 b 6 = 3 5 a 2 b 6 LCD= 2 3 5 a 3 b 5 = 30a 3 b 6 Each denominator is already factored. LCD = z(z + 6)

9. Slide 7.2- 9 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley continued c. m 2 – 16, m 2 + 8m + 16 Factor. = (m +4)(m – 4) LCD m 2 – 16 m 2 + 8m + 16= (m +4) 2 = (m +4) 2 (m – 4) d. x 2 – 2x + 1, x 2 – 4x + 3, 4x – 4 x 2 – 2x + 1= (x – 1)(x – 1) x 2 – 4x + 3= (x – 1)(x – 3) 4x – 4= 4(x – 1) LCD= 4(x – 1) 2 (x – 3)

10. Slide 7.2- 10 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 3 Add and subtract rational expressions with different denominators.

11. Slide 7.2- 11 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Add or subtract as indicated. a. b. Example 3

12. Slide 7.2- 12 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Subtract. a. The denominators are already the same for both rational expressions. The subtraction sign must be applied to both terms in the numerator of the second rational expression.

13. Slide 7.2- 13 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley continued b.

14. Slide 7.2- 14 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Add: To get a common denominator of x – 3, multiply both the numerator and denominator of the second expression by –1. The equivalent answer is Example 5

15. Slide 7.2- 15 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Simplify. Example 6

16. Slide 7.2- 16 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Simplify Example 7

17. Slide 7.2- 17 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Simplify. Example 8

18. Slide 7.2- 18 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Simplify. Example 9

19. Slide 7.2- 19 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Subtract Example 10

20. Slide 7.2- 20 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Add Example 11