Skip to content Skip to navigation

Connexions

You are here: Home » Content » Rational Expressions: Exercise Supplement

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Elementary Algebra"

    Comments:

    "Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This module is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange GroveAs a part of collection: "Elementary Algebra"

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

Recently Viewed

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
Download
x

Download module as:

  • PDF
  • EPUB (what's this?)

    What is an EPUB file?

    EPUB is an electronic book format that can be read on a variety of mobile devices.

    Downloading to a reading device

    For detailed instructions on how to download this content's EPUB to your specific device, click the "(what's this?)" link.

  • More downloads ...
Reuse / Edit
x

Module:

Add to a lens
x

Add module to:

Add to Favorites
x

Add module to:

 

Rational Expressions: Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary:

This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.

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.

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.

This module contains the exercise supplement for the chapter "Rational Expressions".

Exercise Supplement

Rational Expressions ((Reference))

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

Exercise 1

Exercise 2

10xx+6

Exercise 3

Exercise 4

2a+37a+5

Exercise 5

3m2m(m1)

Exercise 6

5r+69r(2r+1)

Exercise 7

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

Exercise 8

11xx29x+18

Exercise 9

y+512y2+28y5

Exercise 10

1612a3+21a26a

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

Exercise 11

45,45

Exercise 12

38,38

Exercise 13

710,710

For the following problems, fill in the missing term.

Exercise 14

3y5=y5

Exercise 15

6a2a+1=2a+1

Exercise 16

x+1x3=x3

Exercise 17

9a+4=a4

Exercise 18

y+3y5=y+5

Exercise 19

6m75m1=6m+7

Exercise 20

2r57r+1=2r5

Reducing Rational Expressions ((Reference))

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

Exercise 21

Exercise 22

164y16

Exercise 23

5m+2510m2+15m

Exercise 24

7+21r7r2+28r

Exercise 25

3a2+4a5a3+6a2

Exercise 26

4x4x2+2x3

Exercise 27

5y+20y216

Exercise 28

4y312y42y23

Exercise 29

6a912a72a714a5

Exercise 30

8x4y8+24x3y94x2y512x3y6

Exercise 31

21y8z10w27y7w2

Exercise 32

35a5b2c4d85abc3d6

Exercise 33

x2+9x+18x3+3x2

Exercise 34

a212a+352a414a3

Exercise 35

y27y+12y24y+3

Exercise 36

m26m16m29m22

Exercise 37

12r27r104r213r+10

Exercise 38

14a25a16a2+9a6

Exercise 39

4a48a34a2

Exercise 40

5m210m3+5m2

Exercise 41

6a15a2

Exercise 42

r5r1

Multiplying and Dividing Rational Expressions ((Reference)) - Adding and Subtracting Rational Expressions ((Reference))

For the following problems, perform the indicated operations.

Exercise 43

x2183x3

Exercise 44

4a2b315x4y510x6y3ab2

Exercise 45

x+6x1x+7x+6

Exercise 46

8a123a+3÷(a+1)24a6

Exercise 47

10m45m24r7+20r3÷m16r8+80r4

Exercise 48

5r+73r+7

Exercise 49

2a3a19a3a1

Exercise 50

9x+74x6+3x+24x6

Exercise 51

15y48y+12y+18y+1

Exercise 52

4a+3+6a5

Exercise 53

7aa+6+5aa8

Exercise 54

x+4x2+x+7x1

Exercise 55

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

Exercise 56

x3(x+2)(x+4)+2x1x+4

Exercise 57

6a+5(2a+1)(4a3)+4a+12a+1

Exercise 58

4x2+3x+2+9x2+6x+8

Exercise 59

6rr2+7r183rr23r+2

Exercise 60

y+3y211y+10y+1y2+3y4

Exercise 61

2a+516a216a+716a212a+2

Exercise 62

7y+46y232y+32+6y102y218y+40

Exercise 63

x2x12x23x+2x2+3x4x23x18

Exercise 64

y21y2+9y+20÷y2+5y6y216

Exercise 65

(r+3)4r+4(r+3)3

Exercise 66

(b+5)3(b+1)2(b+5)2

Exercise 67

(x7)4÷(x7)3x+1

Exercise 68

(4x+9)6÷(4x+9)2(3x+1)4

Exercise 69

5x+2x2+1x4

Exercise 70

2y+4y2+5y1

Exercise 71

y2+4y+4y2+10y+21÷(y+2)

Exercise 72

2x3+4x2+x1x1

Exercise 73

3x+1x2+3x+2+5x+6x2+6x+53x7x22x35

Exercise 74

5a+3b8a2+2abb23ab4a29ab+2b2a+5b4a2+3abb2

Exercise 75

3x2+6x+1010x2+11x6+2x24x+152x211x21

Rational Equations ((Reference))

For the following problems, solve the rational equations.

Exercise 76

4x5+3x115=2925

Exercise 77

6a7+2a321=7721

Exercise 78

5x16+3x+49=89

Exercise 79

4y54+8y+16=6912

Exercise 80

4x1+7x+2=43x2+x2

Exercise 81

5a+3+6a4=9a2a12

Exercise 82

5y3+2y3=3y3

Exercise 83

2m+5m8+9m8=30m8

Exercise 84

r+6r13r+2r1=6r1

Exercise 85

8b+1b7b+5b7=45b7

Exercise 86

Solve z=xxx for s.

Exercise 87

Solve A=P(1+rt) for t.

Exercise 88

Solve 1R=1E+1F for E.

Exercise 89

Solve Q=2mns+t for t.

Exercise 90

Solve I=ER+r for r.

Applications ((Reference))

For the following problems, find the solution.

Exercise 91

When the same number is subtracted from both terms of the fraction 712, the result is 12. What is the number?

Exercise 92

When the same number is added to both terms of the fraction 1315, the result is 89. What is the number?

Exercise 93

When three fourths of a number is added to the reciprocal of the number, the result is 17316. What is the number?

Exercise 94

When one third of a number is added to the reciprocal of the number, the result is 12790. What is the number?

Exercise 95

Person A working alone can complete a job in 9 hours. Person B working alone can complete the same job in 7 hours. How long will it take both people to complete the job working together?

Exercise 96

Debbie can complete an algebra assignment in 34 of an hour. Sandi, who plays her radio while working, can complete the same assignment in 114 hours. If Debbie and Sandi work together, how long will it take them to complete the assignment?

Exercise 97

An inlet pipe can fill a tank in 6 hours and an outlet pipe can drain the tank in 8 hours. If both pipes are open, how long will it take to fill the tank?

Exercise 98

Two pipes can fill a tank in 4 and 5 hours, respectively. How long will it take both pipes to fill the tank?

Exercise 99

The pressure due to surface tension in a spherical bubble is given by P=4Tr, where T is the surface tension of the liquid, and r is the radius of the bubble.
(a) Determine the pressure due to surface tension within a soap bubble of radius 12 inch and surface tension 22.
(b) Determine the radius of a bubble if the pressure due to surface tension is 57.6 and the surface tension is 18.

Exercise 100

The equation 1p+1q=1f relates an objects distance p from a lens and the image distance q from the lens to the focal length f of the lens.
(a) Determine the focal length of a lens in which an object 8 feet away produces an image 6 feet away.
(b) Determine how far an object is from a lens if the focal length of the lens is 10 inches and the image distance is 10 inches.
(c) Determine how far an object will be from a lens that has a focal length of 178 cm and the object distance is 3 cm away from the lens.

Dividing Polynomials ((Reference))

For the following problems, divide the polynomials.

Exercise 101

a2+9a+18 by a+3

Exercise 102

c2+3c88 by c8

Exercise 103

x3+9x2+18x+28 by x+7

Exercise 104

y32y249y6 by y+6

Exercise 105

m4+2m38m2m+2 by m2

Exercise 106

3r217r27 by r7

Exercise 107

a33a256a+10 by a9

Exercise 108

x3x+1 by x+3

Exercise 109

y3+y2y by y+4

Exercise 110

5x6+5x52x4+5x37x28x+6 by x2+x1

Exercise 111

y10y7+3y43y by y4y

Exercise 112

4b73b622b519b4+12b36b2+b+4 by b2+6

Exercise 113

x3+1 by x+1

Exercise 114

a4+6a3+4a2+12a+8 by a2+3a+2

Exercise 115

y10+6y5+9 by y5+3

Content actions

Share content

Share module:

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Reuse / Edit:

Reuse or edit module (?)

Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.