1. Splash Screen

2. Five-Minute Check (over Lesson 8–1) CCSS Then/Now
Example 1: LCM of Monomials and Polynomials
Key Concept: Adding and Subtracting Rational Expressions
Example 2: Monomial Denominators
Example 3: Polynomial Denominators
Example 4: Complex Fractions with Different LCDs
Example 5: Complex Fractions with Same LCD
Lesson Menu

3. A. –3rt
B. –3r
C. 3rt2
D. 4r
5-Minute Check 1

4. A. –3rt
B. –3r
C. 3rt2
D. 4r
5-Minute Check 1

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5-Minute Check 2

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5-Minute Check 2

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5-Minute Check 3

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5-Minute Check 3

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5-Minute Check 4

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5-Minute Check 5

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5-Minute Check 5

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5-Minute Check 6

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5-Minute Check 6

15. Mathematical Practices
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
3 Construct viable arguments and critique the reasoning of others.
CCSS

16. You added and subtracted polynomial expressions.
Determine the LCM of polynomials.
Add and subtract rational expressions.
Then/Now

17. A. Find the LCM of 15a2bc3, 16b5c2, and 20a3c6.
LCM of Monomials and Polynomials
A. Find the LCM of 15a2bc3, 16b5c2, and 20a3c6.
15a2bc3 = 3 ● 5 ● a2 ● b ● c3 Factor the first monomial.
16b5c2 = 24 ● b5 ● c2 Factor the second monomial.
20a3c6 = 22 ● 5 ● a3 ● c Factor the third monomial.
LCM = 3 ● 5 ● 24● a3 ● b5 ● c6
Use each factor the greatest number of times it appears.
Example 1A

18. = 240a3b5c6 Simplify. Answer: LCM of Monomials and Polynomials
Example 1A

19. = 240a3b5c6 Simplify. Answer: 240a3b5c6
LCM of Monomials and Polynomials
= 240a3b5c6 Simplify.
Answer: 240a3b5c6
Example 1A

20. B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
LCM of Monomials and Polynomials
B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
x3 – x2 – 2x = x(x + 1)(x – 2) Factor the first polynomial.
x2 – 4x + 4 = (x – 2)2 Factor the second polynomial.
LCM = x(x + 1)(x – 2)2 Use each factor the greatest number of times it appears as a factor.
Answer:
Example 1B

21. B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
LCM of Monomials and Polynomials
B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
x3 – x2 – 2x = x(x + 1)(x – 2) Factor the first polynomial.
x2 – 4x + 4 = (x – 2)2 Factor the second polynomial.
LCM = x(x + 1)(x – 2)2 Use each factor the greatest number of times it appears as a factor.
Answer: x(x + 1)(x – 2)2
Example 1B

22. A. Find the LCM of 6x2zy3, 9x3y2z2, and 4x2z.
A. x2z
B. 36x2z
C. 36x3y3z2
D. 36xyz
Example 1A

23. A. Find the LCM of 6x2zy3, 9x3y2z2, and 4x2z.
A. x2z
B. 36x2z
C. 36x3y3z2
D. 36xyz
Example 1A

24. B. Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9.
A. x(x + 3)2(x – 1)
B. x(x + 3)(x – 1)
C. x(x – 1)
D. (x + 3)(x – 1)
Example 1B

25. B. Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9.
A. x(x + 3)2(x – 1)
B. x(x + 3)(x – 1)
C. x(x – 1)
D. (x + 3)(x – 1)
Example 1B

26. Concept

27. Simplify each numerator and denominator.
Monomial Denominators
Simplify
The LCD is 42a2b2.
Simplify each numerator and denominator.
Add the numerators.
Example 2

28. Monomial Denominators
Answer:
Example 2

29. Monomial Denominators
Answer:
Example 2

30. Simplify A. B. C. D.
Example 2

31. Simplify A. B. C. D.
Example 2

32. Factor the denominators.
Polynomial Denominators
Simplify
Factor the denominators.
The LCD
is 6(x – 5).
Subtract the numerators.
Example 3

33. Distributive Property
Polynomial Denominators
Distributive Property
Combine like terms.
Simplify.
Simplify.
Answer:
Example 3

34. Distributive Property
Polynomial Denominators
Distributive Property
Combine like terms.
Simplify.
Simplify.
Answer:
Example 3

35. Simplify A. B. C. D.
Example 3

36. Simplify A. B. C. D.
Example 3

37. The LCD of the numerator is ab. The LCD of the denominator is b.
Complex Fractions with Different LCDs
Simplify
The LCD of the numerator is ab. The LCD of the denominator is b.
Example 4

38. Simplify the numerator and denominator.
Complex Fractions with Different LCDs
Simplify the numerator and denominator.
Write as a division expression.
Multiply by the reciprocal of the divisor.
Simplify.
Example 4

39. Complex Fractions with Different LCDs
Answer:
Example 4

40. Complex Fractions with Different LCDs
Answer:
Example 4

41. Simplify
A. B. –1
C. D.
Example 4

42. Simplify
A. B. –1
C. D.
Example 4

43. The LCD of all of the denominators is xy. Multiply by
Complex Fractions with Same LCD
Simplify
The LCD of all of the denominators is xy. Multiply by
Distribute xy.
Example 5

44. Complex Fractions with Same LCD
Answer:
Example 5

45. Complex Fractions with Same LCD
Answer:
Example 5

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

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

48. End of the Lesson