**Rational Expressions ((Reference))**

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

#### Exercise 1

##### Solution

#### Exercise 2

#### Exercise 3

##### Solution

#### Exercise 4

#### Exercise 5

##### Solution

#### Exercise 6

#### Exercise 7

##### Solution

#### Exercise 8

#### Exercise 9

##### Solution

#### Exercise 10

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

#### Exercise 11

##### Solution

#### Exercise 12

#### Exercise 13

##### Solution

For the following problems, fill in the missing term.

#### Exercise 14

#### Exercise 15

##### Solution

#### Exercise 16

#### Exercise 17

##### Solution

9

#### Exercise 18

#### Exercise 19

##### Solution

#### Exercise 20

**Reducing Rational Expressions ((Reference))**

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

#### Exercise 21

##### Solution

#### Exercise 22

#### Exercise 23

##### Solution

#### Exercise 24

#### Exercise 25

##### Solution

#### Exercise 26

#### Exercise 27

##### Solution

#### Exercise 28

#### Exercise 29

##### Solution

#### Exercise 30

#### Exercise 31

##### Solution

#### Exercise 32

#### Exercise 33

##### Solution

#### Exercise 34

#### Exercise 35

##### Solution

#### Exercise 36

#### Exercise 37

##### Solution

#### Exercise 38

#### Exercise 39

##### Solution

#### Exercise 40

#### Exercise 41

##### Solution

#### Exercise 42

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

For the following problems, perform the indicated operations.

#### Exercise 43

##### Solution

#### Exercise 44

#### Exercise 45

##### Solution

#### Exercise 46

#### Exercise 47

##### Solution

#### Exercise 48

#### Exercise 49

##### Solution

#### Exercise 50

#### Exercise 51

##### Solution

#### Exercise 52

#### Exercise 53

##### Solution

#### Exercise 54

#### Exercise 55

##### Solution

#### Exercise 56

#### Exercise 57

##### Solution

#### Exercise 58

#### Exercise 59

##### Solution

#### Exercise 60

#### Exercise 61

##### Solution

#### Exercise 62

#### Exercise 63

##### Solution

#### Exercise 64

#### Exercise 65

##### Solution

#### Exercise 66

#### Exercise 67

##### Solution

#### Exercise 68

#### Exercise 69

##### Solution

#### Exercise 70

#### Exercise 71

##### Solution

#### Exercise 72

#### Exercise 73

##### Solution

#### Exercise 74

#### Exercise 75

##### Solution

**Rational Equations ((Reference))**

For the following problems, solve the rational equations.

#### Exercise 76

#### Exercise 77

##### Solution

#### Exercise 78

#### Exercise 79

##### Solution

#### Exercise 80

#### Exercise 81

##### Solution

#### Exercise 82

#### Exercise 83

##### Solution

No solution;

#### Exercise 84

#### Exercise 85

##### Solution

No solution;

#### Exercise 86

Solve

#### Exercise 87

Solve

##### Solution

#### Exercise 88

Solve

#### Exercise 89

Solve

##### Solution

#### Exercise 90

Solve

**Applications ((Reference))**

For the following problems, find the solution.

#### Exercise 91

When the same number is subtracted from both terms of the fraction

##### Solution

2

#### Exercise 92

When the same number is added to both terms of the fraction

#### Exercise 93

When three fourths of a number is added to the reciprocal of the number, the result is

##### Solution

No rational solution.

#### Exercise 94

When one third of a number is added to the reciprocal of the number, the result is

#### 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?

##### Solution

#### Exercise 96

Debbie can complete an algebra assignment in

#### 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?

##### Solution

24 hrs

#### 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

(a) Determine the pressure due to surface tension within a soap bubble of radius

(b) Determine the radius of a bubble if the pressure due to surface tension is 57.6 and the surface tension is 18.

##### Solution

(a) 176 units of pressure; (b)

#### Exercise 100

The equation

(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

**Dividing Polynomials ((Reference))**

For the following problems, divide the polynomials.

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