2. Chapter 6 Section 4

3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Rational Expressions Add rational expressions having the same denominator. Add rational expressions having different denominators. Subtract rational expressions. 6.4 2 3

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Add rational expressions having the same denominator. Slide 6.4-3

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add rational expressions having the same denominator. Adding Rational Expressions (Same Denominator) If and (Q ≠ 0) are rational expressions, then ADD the numerators and keep the same denominator. Slide 6.4-4 Add. Write each answer in lowest terms.

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Add rational expressions having different denominators. Slide 6.4-6

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add rational expressions having different denominators. Adding Rational Expressions (Different Denominators) Step 1: Find the least common denominator (LCD). Step 2: Rewrite each rational expression as an equivalent rational expression with the LCD as the denominator. Step 3: Add the numerators to get the numerator of the sum. The LCD is the denominator of the sum. Step 4: Write in lowest terms using the fundamental property. Slide 6.4-7

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add. Write each answer in lowest terms. Solution: Slide 6.4-8 Adding Rational Expressions (Different Denominators) CLASSROOM EXAMPLE 2

9. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Add. Write the answer in lowest terms. Slide 6.4-9 Adding Rational Expressions CLASSROOM EXAMPLE 3

10. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Add. Write the answer in lowest terms. Slide 6.4-10 Adding Rational Expressions CLASSROOM EXAMPLE 4

11. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add. Write the answer in lowest terms. Solution: Slide 6.4-11 Adding Rational Expressions (Denominators Are Opposites) CLASSROOM EXAMPLE 5

12. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Subtract rational expressions. Slide 6.4-12

13. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Sign errors often occur in subtraction problems. Be sure to use parentheses after the subtraction sign. Slide 6.4-14 Subtracting Rational Expressions (Same Denominator) Subtract. Write the answer in lowest terms. CLASSROOM EXAMPLE 6

14. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Subtract. Write the answer in lowest terms. Solution: Slide 6.4-15 Subtracting Rational Expressions (Different Denominators) CLASSROOM EXAMPLE 7

15. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Slide 6.4-17 Subtracting Rational Expressions Subtract. Write the answer in lowest terms. CLASSROOM EXAMPLE 9

16. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Subtract. Write the answer in lowest terms. Solution: Slide 6.4-16 Subtracting Rational Expressions (Denominators Are Opposites) CLASSROOM EXAMPLE 8