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Splash Screen. Five-Minute Check (over Chapter 7) CCSS Then/Now New Vocabulary Example 1: Simplify a Rational Expression Example 2: Standardized Test Example: Undefined Values Example 3: Simplify Using –1 Key Concept: Multiplying Rational Expressions

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 7) CCSS Then/Now New Vocabulary Example 1: Simplify a Rational Expression Example 2: Standardized Test Example: 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. Content Standards A.APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Mathematical Practices 8 Look for and express regularity in repeated reasoning. CCSS

  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 Undefined Values Read the Test Item You want to determine which values of p make the denominator equal to 0. Example 2

  17. Undefined Values Solve the Test 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. End of the Lesson

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