1. Splash Screen

2. Lesson Menu 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

3. Over Chapter 7 5-Minute Check 1 A.2.4849 B.1.9459 C.0.7831 D.0.5389 Evaluate log 12 7.

4. Over Chapter 7 5-Minute Check 2 A. B. C. D.

5. Over Chapter 7 5-Minute Check 3 A.6 B.7 C.8 D.9 Solve log 3 (x 2 – 12) = log 3 4x.

6. Over Chapter 7 5-Minute Check 4 A.–0.5108 B.–0.2197 C.0.2197 D.0.4979 Solve 5e x – 3 = 0.

7. Over Chapter 7 5-Minute Check 5 A.about 42 years ago B.about 34 years ago C.exactly 29 years ago D.about 24 years ago 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 = Pe rt.

8. Over Chapter 7 5-Minute Check 6 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 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.

9. CCSS 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.

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

11. Vocabulary rational expression complex fraction

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

13. Example 1B Simplify a Rational Expression Just as with a fraction, a rational expression is undefined if the denominator equals zero. 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. The original factored denominator is (y + 7)(y – 3)(y + 3). B.Under what conditions is the expression undefined?

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

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

16. Example 2 Read the Test Item You want to determine which values of p make the denominator equal to 0. For what value(s) of p is undefined? A5B–3, 5 C3, –5D5, 1, –3 Undefined Values

17. Example 2 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. Answer: B p 2 – 2p –15 = (p – 5)(p + 3)Factor the denominator. p – 5= 0 or p + 3= 0Zero Product Property p= 5p= –3Solve each equation. Undefined Values

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

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

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

21. Concept

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

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

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

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

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

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

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

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

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

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

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

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

34. Example 6 Simplify. A.eB. C.eD.

35. End of the Lesson