2. CHAPTER 6 Rational Expressions and Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 6.1Multiplying and Simplifying Rational Expressions 6.2Division and Reciprocals 6.3Least Common Multiples and Denominators 6.4Adding Rational Expressions 6.5Subtracting Rational Expressions 6.6Complex Rational Expressions 6.7Solving Rational Equations 6.8Applications Using Rational 6.9Variation and Applications

3. OBJECTIVES 6.5 Subtracting Rational Expressions Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aSubtract rational expressions. bSimplify combined additions and subtractions of rational expressions.

4. 6.5 Subtracting Rational Expressions Subtracting Rational Expressions with Like Denominators Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. To subtract when the denominators are the same, subtract the numerators and keep the same denominator. Then simplify if possible.

5. EXAMPLE 6.5 Subtracting Rational Expressions a Subtract rational expressions. 2Subtract: Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

6. 6.5 Subtracting Rational Expressions Subtracting Rational Expressions with Different Denominators Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. To subtract rational expressions with different denominators: 1. Find the LCM of the denominators. This is the least common denominator (LCD). 2. For each rational expression, find an equivalent expression with the LCD. To do so, multiply by 1 using a symbol for 1 made up of factors of the LCD that are missing from the original denominator. 3. Subtract the numerators. Write the difference over the LCD. 4. Simplify if possible.

7. EXAMPLE 6.5 Subtracting Rational Expressions a Subtract rational expressions. 3Subtract: Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

8. EXAMPLE 6.5 Subtracting Rational Expressions a Subtract rational expressions. 3Subtract: Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

9. EXAMPLE 6.5 Subtracting Rational Expressions a Subtract rational expressions. 6Subtract: Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

10. EXAMPLE Solution 6.5 Subtracting Rational Expressions a Subtract rational expressions. 6 Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

11. EXAMPLE Solution 6.5 Subtracting Rational Expressions a Subtract rational expressions. 6 Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

12. EXAMPLE 6.5 Subtracting Rational Expressions a Subtract rational expressions. 7Subtract: Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Factoring 64 – p 2, we get (8 – p)(8 + p).Note that the factors 8 – p in the first denominator and p – 8 in the second denominator are opposites.

13. EXAMPLE Solution 6.5 Subtracting Rational Expressions a Subtract rational expressions. 7 Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

14. EXAMPLE Solution 6.5 Subtracting Rational Expressions a Subtract rational expressions. 7 Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

15. EXAMPLE 6.5 Subtracting Rational Expressions b Simplify combined additions and subtractions of rational expressions. 8Perform the indicated operations and simplify: Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

16. EXAMPLE Solution 6.5 Subtracting Rational Expressions b Simplify combined additions and subtractions of rational expressions. 8 Slide 16Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

17. EXAMPLE 6.5 Subtracting Rational Expressions b Simplify combined additions and subtractions of rational expressions. 9Perform the indicated operations and simplify: Slide 17Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

18. EXAMPLE Solution 6.5 Subtracting Rational Expressions b Simplify combined additions and subtractions of rational expressions. 9 Slide 18Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

19. EXAMPLE Solution 6.5 Subtracting Rational Expressions b Simplify combined additions and subtractions of rational expressions. 9 Slide 19Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.