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Then/Now

You factored polynomials. Simplify rational expressions. Simplify complex fractions. Then/Now. rational expression complex fraction. Vocabulary. A. Simplify. Eliminate common factors. ●. Answer: . Simplify a Rational Expression. Look for common factors. Simplify. Example 1A.

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Then/Now

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

  2. rational expression • complex fraction Vocabulary

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

  4. 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

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

  6. 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

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

  8. Determine 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

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

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

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

  12. Concept

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

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

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

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

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

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

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

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

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

  22. A. B. C. D. Example 5B

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

  24. –1 Factor. Answer: Simplify Complex Fractions Simplify. Example 6

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

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