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Lesson Menu Five-Minute Check (over Lesson 9–1) 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

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

Over Lesson 9–1 A.A B.B C.C D.D 5-Minute Check 2 A. B. C. D.

Over Lesson 9–1 A.A B.B C.C D.D 5-Minute Check 3 A. B. C. D.

Over Lesson 9–1 A.A B.B C.C D.D 5-Minute Check 4 A. B. C. D.

Over Lesson 9–1 A.A B.B C.C D.D 5-Minute Check 5 A. B. C. D.

Over Lesson 9–1 A.A B.B C.C D.D 5-Minute Check 6 A. B. C. D.

Then/Now You added and subtracted polynomial expressions. (Lesson 6–2) Determine the LCM of polynomials. Add and subtract rational expressions.

Example 1A LCM of Monomials and Polynomials A. Find the LCM of 15a 2 bc 3, 16b 5 c 2, and 20a 3 c 6. 15a 2 bc 3 = 3 ● 5 ● a 2 ● b ● c 3 Factor the first monomial. 16b 5 c 2 = 2 4 ● b 5 ● c 2 Factor the second monomial. 20a 3 c 6 = 2 2 ● 5 ● a 3 ● c 6 Factor the third monomial. LCM= 3 ● 5 ● 2 4 ● a 3 ● b 5 ● c 6 Use each factor the greatest number of times it appears.

Example 1A LCM of Monomials and Polynomials Answer: 240a 3 b 5 c 6 = 240a 3 b 5 c 6 Simplify.

Example 1B LCM of Monomials and Polynomials B. Find the LCM of x 3 – x 2 – 2x and x 2 – 4x + 4. LCM = x(x – 2) 2 (x + 1)Use each factor the greatest number of times it appears as a factor. x 3 – x 2 – 2x=x(x – 2)(x + 1)Factor the first polynomial. x 2 – 4x + 4=(x – 2) 2 Factor the second polynomial. Answer: x(x – 2) 2 (x + 1)

A.A B.B C.C D.D Example 1A A.x 2 z B.36x 2 z C.36x 3 y 3 z 2 D.36xyz A. Find the LCM of 6x 2 zy 3, 9x 3 y 2 z 2, and 4x 2 z.

A.A B.B C.C D.D Example 1B 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 x 3 + 2x 2 – 3x and x 2 + 6x + 9.

Concept

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

Example 2 Monomial Denominators Answer:

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

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

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

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

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

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

Example 4 Complex Fractions with Different LCDs Answer:

A.A B.B C.C D.D Example 4 Simplify. A.B.–1 C.D.

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

Example 5 Complex Fractions with Same LCD Answer:

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

End of the Lesson