2. Chapter 6 Section 5

3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Complex Fractions Simplify a complex fraction by multiplying numerator and denominator by the least common denominator (Method 2). Simplify rational expressions with negative exponents. 6.5 2

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Complex Fractions. The quotient of two mixed numbers can be written as a fraction. Complex Fraction A fraction with fractions in the numerator and/or denominator is called a complex fraction. Numerator of complex fraction Main fraction bar Denominator of complex fraction Slide 6.5-3

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Simplify a complex fraction by multiplying numerator and denominator by the least common denominator. (Method 2 in our Text) Slide 6.5-9

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Simplify each complex fraction. Slide 6.5-11 Simplifying Complex Fractions (Method 2) CLASSROOM EXAMPLE 4

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc. This technique utilizes the Fundamental Law of Fractions. Method 2 from our Text Simplifying a Complex Fraction Step 1: Find the LCD of all fractions within the complex fraction. Step 2: Multiply both the numerator and denominator of the complex fraction by this LCD using the distributive property as necessary. Write in lowest terms. Slide 6.5-10

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Simplify the complex fraction. Solution: Slide 6.5-12 Simplifying a Complex Fraction (Method 2) CLASSROOM EXAMPLE 5 LCD = a 2 b 2

9. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution : Simplify the complex fraction. Slide 6.5-8 Simplifying a Complex Fraction CLASSROOM EXAMPLE 3 LCD = (a+1)(b-2)(a+3) (a+1)(b-2)(a+3)

10. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Simplify each complex fraction. Slide 6.5-13 Deciding on a Method and Simplifying Complex Fractions Solution: CLASSROOM EXAMPLE 6 Note: One term distribute once, two terms distribute twice Ex 1 Ex 2

11. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Simplify rational expressions with negative exponents. Objective 2 Slide 6.5-10

12. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Simplify the expression, using only positive exponents in the answer. LCD = a 2 b 3 Slide 6.5-11 CLASSROOM EXAMPLE 7 Simplifying Rational Expressions with Negative Exponents Solution: Negative exponent means take the reciprocal of the base.

13. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Write with positive exponents. LCD = x 3 y Slide 6.5-12 CLASSROOM EXAMPLE 7 You Try It Simplify the expression, using only positive exponents in the answer. Solution: