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LESSON 8–1

LESSON 8–1. Multiplying and Dividing Rational Expressions. Five-Minute Check (over Chapter 7) TEKS Then/Now New Vocabulary Example 1: Simplify a Rational Expression Example 2: Determine Undefined Values Example 3: Simplify Using –1 Key Concept: Multiplying Rational Expressions

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LESSON 8–1

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  1. LESSON 8–1 Multiplying and Dividing Rational Expressions

  2. Five-Minute Check (over Chapter 7) TEKS Then/Now New Vocabulary Example 1: Simplify a Rational Expression Example 2: Determine Undefined Values Example 3: Simplify Using –1 Key Concept: Multiplying Rational Expressions Example 4: Multiply and Divide Rational Expressions Example 5: Polynomials in the Numerator and Denominator Example 6: Simplify Complex Fractions Lesson Menu

  3. Evaluate log12 7. A. 2.4849 B. 1.9459 C. 0.7831 D. 0.5389 5-Minute Check 1

  4. A. B. C. D. 5-Minute Check 2

  5. Solve log3 (x2 – 12) = log3 4x. A. 6 B. 7 C. 8 D. 9 5-Minute Check 3

  6. Solve 5ex – 3 = 0. A. –0.5108 B. –0.2197 C. 0.2197 D. 0.4979 5-Minute Check 4

  7. Suppose $200 was deposited in a bank account and it is now worth $1100. If the annual interest rate was 5% compounded continuously, how long ago was the account started? Use the formula A = Pert. A. about 42 years ago B. about 34 years ago C. exactly 29 years ago D. about 24 years ago 5-Minute Check 5

  8. Suppose the population of New York State grows at a rate of 0.3% compounded continuously. In 2006, the population was 19.3 million. Write an equation that represents the population and predict the population in after t years 2020. A.y = 19.3e(0.003)t; about 20.1 million B.y = 19.3e(0.03)t; about 29.4 million C.y = 19.3e(1.003)t; about 52.6 million D.y = 19.3e(1.3)t; about 70.8 million 5-Minute Check 6

  9. Targeted TEKS A2.7(F) Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two. Mathematical Processes A2.1(E), A2.1(F) TEKS

  10. You factored polynomials. • Simplify rational expressions. • Simplify complex fractions. Then/Now

  11. rational expression • complex fraction Vocabulary

  12. A. Simplify . Eliminate common factors. ● Answer: Simplify a Rational Expression Look for common factors. Simplify. Example 1A

  13. B. Under what conditions is the expression undefined? Simplify a Rational Expression Just as with a fraction, a rational expression is undefined if the denominator equals zero. The original factored denominator is (y + 7)(y – 3)(y + 3). Answer: The values that would make the denominator equal to 0 are –7, 3, and –3. So the expression is undefined at y = –7, y = 3, and y = –3. Example 1B

  14. A. Simplify . A. B. C. D. Example 1A

  15. B. Under what conditions is the expression undefined? A. x = 4 or x = –4 B.x = –5 or x = 4 C.x = –5, x = 4, or x = –4 D.x = –5 Example 1B

  16. For what value(s) of p is undefined? A 5 B –3, 5 C 3, –5 D 5, 1, –3 Determine Undefined Values Read the Item You want to determine which values of p make the denominator equal to 0. Example 2

  17. Determine Undefined Values Solve the Item Look at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator. p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator. p – 5 = 0 or p + 3 = 0 Zero Product Property p = 5 p = –3 Solve each equation. Answer: B Example 2

  18. For what value(s) of p is undefined? A. –5, –3, –2 B. –5 C. 5 D. –5, –3 Example 2

  19. Simplify . Simplify Using –1 Factor the numerator and the denominator. b – 2 = –(–b + 2) or –1(2 – b) Simplify. Answer: –a Example 3

  20. Simplify . A.y – x B.y C.x D. –x Example 3

  21. Concept

  22. A.Simplify . Answer: Multiply and Divide Rational Expressions Simplify. Simplify. Example 4A

  23. B. Simplify Multiply by the reciprocal of the divisor. Simplify. Multiply and Divide Rational Expressions Example 4B

  24. Answer: Simplify. Multiply and Divide Rational Expressions Example 4B

  25. A. Simplify . A. B. C. D. Example 4A

  26. B. Simplify . A. AnsA B. AnsB C. AnsC D. AnsD Example 4B

  27. A.Simplify . Factor. Polynomials in the Numerator and Denominator 1 + k = k + 1,1 – k = –1(k – 1) = –1 Simplify. Answer: –1 Example 5A

  28. B.Simplify . Polynomials in the Numerator and Denominator Multiply by the reciprocal of the divisor. Factor. Example 5B

  29. Answer: Polynomials in the Numerator and Denominator Simplify. Example 5B

  30. A. Simplify . A. B. C.1 D.–1 Example 5A

  31. A. B. C. D. Example 5B

  32. Simplify . Express as a division expression. Multiply by the reciprocal of the divisor. Simplify Complex Fractions Example 6

  33. –1 Factor. Answer: Simplify Complex Fractions Simplify. Example 6

  34. Simplify . A. e B. C. e D. Example 6

  35. LESSON 8–1 Multiplying and Dividing Rational Expressions

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