Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–1) Then/Now Example 1:LCM of Monomials...
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Over Lesson 9–1 A.A B.B C.C D.D 5-Minute Check 1 A.–3rt B.–3r C.3rt 2 D.4r
Transcript of Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–1) Then/Now Example 1:LCM of Monomials...
Five-Minute Check (over Lesson 9–1)Then/NowExample 1:LCM of Monomials and PolynomialsKey Concept: Adding and Subtracting Rational ExpressionsExample 2:Monomial DenominatorsExample 3:Polynomial DenominatorsExample 4:Complex Fractions with Different LCDsExample 5:Complex Fractions with Same LCD
Over Lesson 9–1
A. AB. BC. CD. D
A B C D
0% 0%0%0%
A. –3rt
B. –3r
C. 3rt2
D. 4r
Over Lesson 9–1
A. AB. BC. CD. D
A B C D
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A.
B.
C.
D.
Over Lesson 9–1
A. AB. BC. CD. D
A B C D
0% 0%0%0%
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B.
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Over Lesson 9–1
A. AB. BC. CD. D
A B C D
0% 0%0%0%
A.
B.
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D.
Over Lesson 9–1
A. AB. BC. CD. D
A B C D
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B.
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D.
Over Lesson 9–1
A. AB. BC. CD. D
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You added and subtracted polynomial expressions. (Lesson 6–2)
• Determine the LCM of polynomials.
• Add and subtract rational expressions.
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 secondmonomial.
20a3c6 = 22 ● 5 ● a3 ● c6 Factor the third monomial.
LCM = 3 ● 5 ● 24● a3
● b5 ● c6 Use each factor thegreatest number of timesit appears.
LCM of Monomials and Polynomials
Answer: 240a3b5c6
= 240a3b5c6 Simplify.
LCM of Monomials and Polynomials
B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
LCM = x(x – 2)2(x + 1)Use each factor the greatest number of times it appears as a factor.
x3 – x2 – 2x = x(x – 2)(x + 1) Factor the firstpolynomial.
x2 – 4x + 4 = (x – 2)2 Factor the secondpolynomial.
Answer: x(x – 2)2(x + 1)
A. AB. BC. CD. D
A B C D
0% 0%0%0%
A. x2z
B. 36x2z
C. 36x3y3z2
D. 36xyz
A. Find the LCM of 6x2zy3, 9x3y2z2, and 4x2z.
A. AB. BC. CD. D
A B C D
0% 0%0%0%
A. x(x + 3)2(x – 1)
B. x(x + 3)(x – 1)
C. x(x – 1)
D. (x + 3)(x – 1)
B. Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9.
Monomial Denominators
The LCD is 42a2b2.
Simplify .
Simplify each numerator and denominator.
Add the numerators.
Monomial Denominators
Answer:
A. AB. BC. CD. D
A B C D
0% 0%0%0%
Simplify .
A.
B.
C.
D.
Polynomial Denominators
Factor the denominators.
Simplify .
Subtract the numerators.
The LCD is 6(x – 5).
Polynomial Denominators
Distributive Property
Combine like terms.
Simplify.
Simplify.Answer:
A. AB. BC. CD. D
A B C D
0% 0%0%0%
Simplify .
A.
B.
C.
D.
Complex Fractions with Different LCDs
The LCD of the numerator is ab. The LCD of the denominator is b.
Simplify .
Complex Fractions with Different LCDs
Write as a division expression.
Simplify the numerator and denominator.
Multiply by the reciprocal of the divisor.
Simplify.
Complex Fractions with Different LCDs
Answer:
A. AB. BC. CD. D
A B C D
0% 0%0%0%
Simplify .
A. B. –1
C. D.
Complex Fractions with Same LCD
The LCD of all of the
denominators is xy.
Multiply by
Simplify
Distribute xy.
Complex Fractions with Same LCD
Answer:
A. AB. BC. CD. D
A B C D
0% 0%0%0%
Simplify
A. B.
C. D.
