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<para>This module is from<link document="col10614">Elementary Algebra</link>by Denny Burzynski and Wade Ellis, Jr.</para><para>A detailed study of arithmetic operations with rational expressions is presented in this chapter, beginning with the definition of a rational expression and then proceeding immediately to a discussion of the domain. The process of reducing a rational expression and illustrations of multiplying, dividing, adding, and subtracting rational expressions are also included. Since the operations of addition and subtraction can cause the most difficulty, they are given particular attention. We have tried to make the written explanation of the examples clearer by using a "freeze frame" approach, which walks the student through the operation step by step.</para><para>The five-step method of solving applied problems is included in this chapter to show the problem-solving approach to number problems, work problems, and geometry problems. The chapter also illustrates simplification of complex rational expressions, using the combine-divide method and the LCD-multiply-divide method.</para><para>This module contains the exercise supplement for the chapter "Rational Expressions".</para>

Exercise supplement

Rational expressions ( [link] )

For the following problems, find the domain of each rational expression.

x + 1 2 x 5

x 5 2

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3 m 2 m ( m 1 )

m 0 , 1

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s s ( s + 8 ) ( 4 s + 7 )

s 8 , 7 4 , 0

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11 x x 2 9 x + 18

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y + 5 12 y 2 + 28 y 5

y 1 6 , 5 2

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16 12 a 3 + 21 a 2 6 a

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For the following problems, show that the fractions are equivalent.

4 5 , 4 5

( 4 · 5 ) = 20 , 4 ( 5 ) = 20

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7 10 , 7 10

( 7 · 10 ) = 70 , 7 ( 10 ) = 70

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For the following problems, fill in the missing term.

6 a 2 a + 1 = 2 a + 1

6 a

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x + 1 x 3 = x 3

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9 a + 4 = a 4

9

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y + 3 y 5 = y + 5

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6 m 7 5 m 1 = 6 m + 7

5 m + 1

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2 r 5 7 r + 1 = 2 r 5

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Reducing rational expressions ( [link] )

For the following problems, reduce the rational expressions to lowest terms.

5 m + 25 10 m 2 + 15 m

m + 5 m ( 2 m + 3 )

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3 a 2 + 4 a 5 a 3 + 6 a 2

3 a + 4 a ( 5 a + 6 )

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4 x 4 x 2 + 2 x 3

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5 y + 20 y 2 16

5 y 4

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4 y 3 12 y 4 2 y 2 3

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6 a 9 12 a 7 2 a 7 14 a 5

3 a 2 ( a 2 2 ) a 2 7

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8 x 4 y 8 + 24 x 3 y 9 4 x 2 y 5 12 x 3 y 6

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21 y 8 z 10 w 2 7 y 7 w 2

3 y z 10

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35 a 5 b 2 c 4 d 8 5 a b c 3 d 6

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x 2 + 9 x + 18 x 3 + 3 x 2

x + 6 x 2

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a 2 - 12 a + 35 2 a 4 14 a 3

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y 2 7 y + 12 y 2 4 y + 3

y 4 y 1

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m 2 6 m 16 m 2 9 m 22

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12 r 2 7 r 10 4 r 2 13 r + 10

3 r + 2 r 2

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14 a 2 5 a 1 6 a 2 + 9 a 6

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4 a 4 8 a 3 4 a 2

a ( a 2 )

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6 a 1 5 a 2

6 a + 1 5 a + 2

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Multiplying and dividing rational expressions ( [link] ) - adding and subtracting rational expressions ( [link] )

For the following problems, perform the indicated operations.

x 2 18 · 3 x 3

1 6 x

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4 a 2 b 3 15 x 4 y 5 · 10 x 6 y 3 a b 2

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x + 6 x 1 · x + 7 x + 6

x + 7 x 1

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8 a 12 3 a + 3 ÷ ( a + 1 ) 2 4 a 6

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10 m 4 5 m 2 4 r 7 + 20 r 3 ÷ m 16 r 8 + 80 r 4

20 m r ( 2 m 2 1 )

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2 a 3 a 1 9 a 3 a 1

7 a 3 a 1

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9 x + 7 4 x 6 + 3 x + 2 4 x 6

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15 y 4 8 y + 1 2 y + 1 8 y + 1

13 y 5 8 y + 1

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7 a a + 6 + 5 a a 8

2 a ( 6 a 13 ) ( a + 6 ) ( a 8 )

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x + 4 x 2 + x + 7 x 1

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2 y + 1 y + 4 y + 6 y + 1

y 2 7 y 23 ( y + 4 ) ( y + 1 )

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x 3 ( x + 2 ) ( x + 4 ) + 2 x 1 x + 4

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6 a + 5 ( 2 a + 1 ) ( 4 a 3 ) + 4 a + 1 2 a + 1

2 ( 8 a 2 a + 1 ) ( 2 a + 1 ) ( 4 a 3 )

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4 x 2 + 3 x + 2 + 9 x 2 + 6 x + 8

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6 r r 2 + 7 r 18 3 r r 2 3 r + 2

3 r ( 3 r + 7 ) ( r 1 ) ( r 2 ) ( r + 9 )

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y + 3 y 2 11 y + 10 y + 1 y 2 + 3 y 4

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2 a + 5 16 a 2 1 6 a + 7 16 a 2 12 a + 2

16 a 2 18 a 17 2 ( 4 a 1 ) ( 4 a + 1 ) ( 2 a 1 )

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7 y + 4 6 y 2 32 y + 32 + 6 y 10 2 y 2 18 y + 40

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x 2 x 12 x 2 3 x + 2 · x 2 + 3 x 4 x 2 3 x 18

( x + 4 ) ( x 4 ) ( x 2 ) ( x 6 )

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y 2 1 y 2 + 9 y + 20 ÷ y 2 + 5 y 6 y 2 16

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( r + 3 ) 4 · r + 4 ( r + 3 ) 3

( r + 3 ) ( r + 4 )

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( b + 5 ) 3 · ( b + 1 ) 2 ( b + 5 ) 2

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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