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Chapter 8A1Glencoe Algebra 2

Answers

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Answers(Anticipation Guide and Lesson 8-1)

8-1 Lesson Reading GuideMultiplying and Dividing Rational Expressions

Chapter 8

5

Glencoe Algebra 2

Lesson 8-1

Get Ready for the LessonRead the introduction to Lesson 8-1 in your textbook. • Suppose that the Goodie Shoppe also sells a candy mixture made with

4 pounds of chocolate mints and 3 pounds of caramels, then

of the mixture is mints and of the mixture is caramels. • If the store manager adds another ypounds of mints to the mixture, what fraction of the mixture will be mints?Read the Lesson

1. a.In order to simplify a rational number or rational expression, the

numerator and and divide both of them by their b.A rational expression is undefined when its is equal to . To find the values that make the expression undefined, completely the original and set each factor equal to .

2. a.To multiply two rational expressions, the and

multiply the denominators. b.To divide two rational expressions, by the of the .

3. a.Which of the following expressions are complex fractions?

ii, iv, v i. ii. iii. iv. v. b.Does a complex fraction express a multiplication or division problem? division How is multiplication used in simplifying a complex fraction?

Sample answer:To divide the numerator of the complex fraction by the denominator,multiply the numerator by the reciprocal of the denominator.

Remember What You Learned

4. One way to remember something new is to see how it is similar to something you already know. How can your knowledge of division of fractions in arithmetic help you to

understand how to divide rational expressions?Sample answer:To divide rationalexpressions, multiply the first expression by the reciprocal of thesecond.This is the same "invert and multiply" process that is used whendividing arithmetic fractions.

?r 2 925
?r? 35
?z? z1 zr?5 ?r?5 ?3 8 ??15 6 7 ?12 divisorreciprocal multiply numerators multiply 0 denominator factor 0 denominator greatest common factor denominator factor

4 ?y?7 ?y

?3 7 47

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.NAME ______________________________________________ DATE______________ PERIOD _____

8 Anticipation GuideRational Expressions and Equations

Chapter 8

3

Glencoe Algebra 2

Before you begin Chapter 8

• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 8

• Reread each statement and complete the last column by entering an A or a D. • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a piece of paper to write an example of why you disagree. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME ______________________________________________ DATE______________ PERIOD _____Step 1

STEP 1STEP 2

A, D, or NSStatementA or D

1.Since a denominator cannot equal 0, the expression

A is undefined for x??5.

2.To divide two rational expressions, multiply by the reciprocal

of the divisor. A

3.The least common multiple of three monomials is found by

multiplying the monomials together. D

4.Before adding two rational expressions, a common

denominator must be found. A

5.The graph of a rational function containing an asymptote

will be symmetric over the asymptote. D

6.Since f(x) ?can be simplified to f(x) ?m?2,the graph off(x) will be the straight line defined byy?m?2.

D

7.y?kxyzis an example of a joint variation if k,x,y, and zare

all not equal to 0. A

8.The shape of the graph of y??3x

2 ?2x?4 can only be determined by graphing the function. D

9.Because the graph of an absolute value function is in the

shape of a V, the graph of y??x??4 will also be in the shape A of a V.

10.When solving rational equations, solutions that result in a

zero in the denominator must be excluded. A (m?4)(m?2)?? m?43x 2 (x?1) x?5

Step 2

Chapter Resources

Chapter 8A2Glencoe Algebra 2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Study Guide and Intervention

(continued)

Multiplying and Dividing Rational Expressions

NAME ______________________________________________ DATE______________ PERIOD _____

Chapter 8

7

Glencoe Algebra 2

Lesson 8-1

Simplify Complex Fractions

A complex fractionis a rational expression whose

numerator and/or denominator contains a rational expression. To simplify a complex fraction, first rewrite it as a division problem.

Simplify .

Express as a division problem.

Multiply by the reciprocal of the divisor.

Factor.

Simplify.

Simplify.

1. 2. 3.

(b?1) 2 4. 5. 6. a?4 7. x?3 8. 9. 1 ?x?5 x 2 ?x?2 x 3 ?6x 2 ?x?30 x?1?x?3 b?4 ??(b?1)(b?2) ?b 2 ?b? 6b2 ?8 ?b 2b 2? ?b 1? 62
?2x 2 x? ?9x 1?9 ???10 5x x 2 2 ?1 79
xx 26
?a a 2 ?1 26
???a a 2 2 ?3 aa 24
1 ??(x?3)(x?2) ?x 2 ?x? 6x4 ?9 ???x 2 3?2x x?8

2(b?10)

??b(3b?1) ?b 2 b 2 100
???3b 2 ?3 21
bb?10 ?3b b 2 ?1 2 ???3b 2 b b1 ?2 ac 7 by ?a x 2 2 b yc 23
??ca 4 xb 22
y xyz? a 5 ?x a 3 2 y b 2 2 z ??a 3bx 22
y s 3 ?s?3(3s?1)s 4 ??s(3s?1)(s?3)s 4 ??3s 2 ?8s?33s?1 s3s 2 ?8s?3 s 4 3s?1? s ?3s s?1 ???3s 2 s8 4 s?3 ?3s s?1 ???3s 2 s8 4 s?3 1 1 1s 3 8-1

ExercisesExample

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 8-1

Chapter 8

6

Glencoe Algebra 2

Simplify Rational Expressions

A ratio of two polynomial expressions is a rational expression. To simplify a rational expression, divide both the numerator and the denominator by their greatest common factor (GCF). Multiplying Rational ExpressionsFor all rational expressions and , ??, if b?0 and d?0. Dividing Rational ExpressionsFor all rational expressions and , ??, if b?0, c?0, and d?0.

Simplify each expression.

a. b.? c.?

Simplify each expression.

1. 22
0a ab b 2 4 3 2. 3. 4.? 2m 2 (m?1) 5.? 6.? m 7.?

8.?9.?

quotesdbs_dbs17.pdfusesText_23

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