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Section 3

Chapter 7. Section 3. Complex Fractions. Simplify complex fractions by simplifying the numerator and denominator (Method 1). Simplify complex fractions by multiplying by a common denominator (Method 2). Compare the two methods of simplifying complex fractions.

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Section 3

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  1. Chapter 7 Section 3

  2. Complex Fractions Simplify complex fractions by simplifying the numerator and denominator (Method 1). Simplify complex fractions by multiplying by a common denominator (Method 2). Compare the two methods of simplifying complex fractions. Simplify rational expressions with negative exponents. 7.3

  3. A complex fractionis a quotient having a fraction in the numerator, denominator, or both. Complex Fractions Slide 7.3- 3

  4. Simplify complex fractions by simplifying the numerator and denominator (Method 1). Objective 1 Slide 7.3- 4

  5. Simplify complex fractions by simplifying the numerator and denominator (Method 1). Slide 7.3- 5

  6. Use Method 1 to simplify the complex fraction. CLASSROOM EXAMPLE 1 Simplifying Complex Fractions (Method 1) Both the numerator and denominator are already simplified. Solution: Write as a division problem. Multiply by the reciprocal. Multiply. Slide 7.3- 6

  7. Use Method 1 to simplify the complex fraction. CLASSROOM EXAMPLE 1 Simplifying Complex Fractions (Method 1) (cont’d) Simplify the numerator and denominator. Solution: Slide 7.3- 7

  8. Simplify complex fractions by multiplying by a common denominator (Method 2). Objective 2 Slide 7.3- 8

  9. Simplify complex fractions by multiplying by a common denominator (Method 2). Slide 7.3- 9

  10. Use Method 2 to simplify the complex fraction. CLASSROOM EXAMPLE 2 Simplifying Complex Fractions (Method 2) The LCD is x. Multiply the numerator and denominator by x. Solution: Slide 7.3- 10

  11. Use Method 2 to simplify the complex fraction. CLASSROOM EXAMPLE 2 Simplifying Complex Fractions (Method 2) (cont’d) Multiply the numerator and denominator by the LCD y(y + 1). Solution: Slide 7.3- 11

  12. Compare the two methods of simplifying complex fractions. Objective 3 Slide 7.3- 12

  13. CLASSROOM EXAMPLE 3 Simplifying Complex Fractions (Both Methods) Simplify the complex fraction by both methods. Method 2 Method 1 Solution: Slide 7.3- 13

  14. CLASSROOM EXAMPLE 3 Simplifying Complex Fractions (Both Methods) (cont’d) Simplify the complex fraction by both methods. Method 1 Solution: LCD = ab LCD = a2b2 Slide 7.3- 14

  15. CLASSROOM EXAMPLE 3 Simplifying Complex Fractions (Both Methods) (cont’d) Simplify the complex fraction by both methods. Method 2 Solution: LCD of the numerator and denominator is a2b2. Slide 7.3- 15

  16. Simplify rational expressions with negative exponents. Objective 4 Slide 7.3- 16

  17. CLASSROOM EXAMPLE 4 Simplifying Rational Expressions with Negative Exponents Simplify the expression, using only positive exponents in the answer. Solution: LCD = a2b3 Slide 7.3- 17

  18. CLASSROOM EXAMPLE 4 Simplifying Rational Expressions with Negative Exponents (cont’d) Simplify the expression, using only positive exponents in the answer. Solution: Write with positive exponents. LCD = x3y Slide 7.3- 18

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