Rational Expressions

1. Rational Expressions Sections 9-3, 9-4, 9-5

2. Multiplying / Dividing Let’s first review how we multiply and divide fractions.

3. Multiplying / Dividing When multiplying/ dividing, do we have to have a common denominator? Nope

4. Multiplying / Dividing Is there anything special that we have to do? Nope

5. Multiplying / Dividing How do we multiply fractions? Multiply numerators and denominators.

6. Multiplying / Dividing Examples:

7. Multiplying / Dividing Examples:

8. Multiplying / Dividing Let’s talk about simplifying. When can we cancel things in the numerator and denominator?

9. Multiplying / Dividing You must have exactly the same factor. x - 3 can only be simplified by x - 3, not by x, not by 3, only by x - 3.

10. Multiplying / Dividing Simplify:

11. Multiplying / Dividing Simplify:

12. Multiplying / Dividing Simplify:

13. Multiplying / Dividing Simplify: factor first

14. Multiplying / Dividing Simplify: cancel

15. Multiplying / Dividing Simplify: factor, then cancel

16. Multiplying / Dividing Simplify: factor, then cancel

17. Multiplying / Dividing Complete wkst 107 Completely simplify each polynomial (numerator and denominator), then cancel.

18. Multiplying / Dividing When multiplying rational expressions, factor each numerator and denominator first, then cancel, then multiply (squish them together).

19. Multiplying / Dividing Steps to multiply: 1)factor completely 2)cancel 3)multiply (squish)

20. Multiplying / Dividing Multiply: We have nothing to factor so just cancel and multiply.

21. Multiplying / Dividing Multiply:

22. Multiplying / Dividing Multiply:

23. Multiplying / Dividing Factor:

24. Multiplying / Dividing Cancel:

25. Multiplying / Dividing Multiply:

26. Multiplying / Dividing Realize: sometimes you may see people go ahead and multiply (such as the last numerator), you don’t have to do this for me. Just be able to recognize it if you see it.

27. Multiplying / Dividing Work on wkst 111

28. Multiplying / Dividing Now on to dividing. This is exactly like multiplying, except for ONE step.

29. Multiplying / Dividing How do we divide fractions? We multiply by the reciprocal (inverse) of the divisor (2nd fraction).

30. Multiplying / Dividing Divide:

31. Multiplying / Dividing Divide: first step is flip & multiply.

32. Multiplying / Dividing Divide: Now proceed like a multiplication problem. Factor first, cancel, multiply.

33. Multiplying / Dividing

34. Multiplying / Dividing Simplify

35. Multiplying / Dividing Wkst 113/112 Start on the dividing side first.

36. Adding/Subtracting What do we have to have in order to add or subtract fractions? Right a common denominator.

37. Adding/Subtracting when we talk about CDs, we mean denominators that contain the same factors. To find our CD, we will first factor the ones we have.

38. Adding/Subtracting Then we will multiply each denominator by the factors it is missing to create a CD. Remember, we must also multiply the numerator by that same factor.

39. Adding/Subtracting Find the common denominator for these two rational expressions.

40. Adding/Subtracting

41. Adding/Subtracting

42. Adding/Subtracting Now that we have a CD, we just simplify (we did already) and add the numerators.

43. Adding/Subtracting If we could factor the numerator and denominator, we would to see if we could simplify more.

44. Steps to Add/Subtract Factor denominators Find CD & equivalent fractions Simplify/add/sub numer. Factor numer/denom Cancel

45. Adding/Subtracting Simplify:

46. Adding/Subtracting Factor

47. Adding/Subtracting Find CD We need a factor of (x+2) in the first denominator and a factor of (x+3) in the second denominator.

48. Adding/Subtracting Create equivalent fractions.

49. Adding/Subtracting Simplify the numerators.

50. Adding/Subtracting Subtract. (x2 + 2x) - (2x + 6) = x2 - 6

51. Adding/Subtracting Can we factor the numerator? No, we are done.

52. Adding/Subtracting Simplify:

53. Adding/Subtracting

54. Adding/Subtracting

55. Adding/Subtracting pg. 573 21- 37 odd

56. Adding/Subtracting pg. 573 21- 37 odd

57. Complex Fractions Complex fractions are those fractions whose numerator & denominator both contain fractions. To simplify them, we just multiply by the CD.

58. Complex Fractions Example: What would be the CD? 6 Multiply every term by 6.

59. Complex Fractions Simplify.

60. Complex Fractions Simplify.

61. Complex Fractions Simplify. CD is ? xy

62. Complex Fractions Multiply each term by xy.

63. Complex Fractions Simplfy.

64. Complex Fractions Final answer.

65. Complex Fractions Steps to simplify. Find the CD Multiply EACH term by the CD Cancel and Simplify

66. Complex Fractions Work on Complex Fraction Worksheet

67. Rational Equations Solving Rational Equations would be easy, except for the rational part. How can we get rid of the the fractions?

68. Rational Equations Multiply BOTH SIDES by the common denominator This will be very similar to adding/subtracting rational expressions.

69. Rational Equations Once you have multiplied by the CD, just solve the equation like you would normally. Use your calculator if you want to.

70. Rational Equations Solve:

71. Rational Equations What is the CD? (r - 3)(r + 3)

72. Rational Equations Multiply by (r - 3)(r + 3) on both sides.

73. Rational Equations Simplify & distribute

74. Rational Equations Solve

75. Rational Equations Solve:

76. Rational Equations Common Denominator is 6(x-2)

77. Rational Equations Multiply by 6(x-2)

78. Rational Equations Cancel

79. Rational Equations Simplify

80. Rational Equations Solve

81. Rational Equations Solve

82. Rational Equations Try some on your own pg. 581 6 - 9 => solve them all

83. Rational Equations Assignment pg. 582 13 - 18 all (just solve), 25 - 28 all