Deck 6: Rational Expressions

Question 1

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero.

A)
B)
C)
D)
E) in lowest terms

Answer 1

Question 2

The function gives the number of days it would take two construction crews, working together, to frame a house that crew 1 (working alone) could complete in t days and crew 2 (working alone) could complete in days. If crew 2 could frame a certain house in 20 days, how long would it take both crews working together? Round the answer to the nearest tenth.

A) 10.7 days
B) 1.7 days
C) 12.2 days
D) 9.2 days

Answer 2

9.2 days

Question 3

Perform the division.

A)
B)
C)
D)
E)

Answer 3

Question 4

Determine the domain of the given function.

A)
B)
C)
D)

Question 5

Determine the domain of the given function.

A)
B)
C)
D)

Question 6

Simplify this rational expression. Assume the denominator never equals zero.

A)
B)
C)
D)
E) Does not simplify further.

Question 7

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 8

Simplify this rational expression. Assume the denominator never equals zero.

A) 1
B) 2 a - 8 x
C) 8 x - 2 a
D) -1
E) Does not simplify further.

Question 9

Find any real numbers x which make undefined.

A)
B)
C)
D) defined for all real numbers

Question 10

Simplify:

A)
B)
C)
D)

Question 11

Perform the operations and simplify.

A)
B)
C)
D)

Question 12

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 13

An electric company charges per month plus cents for each kilowatt hour (kwh) of electricity used. Find the average cost per kwh when kwh are used.

A) cents
B) cents
C) cents
D) cents

Question 14

Determine the domain of the given function.

A)
B)
C)
D)

Question 15

Perform the operations.

A)
B)
C)
D)
E)

Question 16

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 17

Perform the indicated division and express your answer in simplest form.

A)
B)
C)
D)
E)

Question 18

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero.

A)
B)
C)
D)
E) in lowest terms

Question 19

Which value of x makes the rational expression undefined?

A)
B)
C)
D)
E) none

Question 20

The average cost c (in dollars) for a company to produce x child car seats is given by the formula . Find the company's average cost to produce a car seat if 1,000 are produced. $ __________

Question 21

Solve the expression.

A)
B)
C)
D)

Question 22

Perform the indicated operation. Simplify the answer if possible.

Question 23

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 24

Simplify.

A)
B)
C)
D)

Question 25

Perform the operation and simplify the result when possible.

A)
B)
C)
D)
E)

Question 26

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 27

Perform the indicated operation.

Question 28

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 29

Simplify.

A)
B)
C)
D)

Question 30

Two denominators are given. Find the LCD. t ² 7 t 8, t ² 64

Question 31

Perform the indicated operations involving rational numbers. Express the final answer in reduced form.

A)
B)
C)
D)
E)

Question 32

Perform the operation. Simplify the answer, if possible.

Question 33

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 34

Solve the equation and check the solution.

A) - 105
B) 105
C) 210
D) - 210
E) no solution

Question 35

Perform the indicated operation and express your answer in simplest form.

A)
B)
C)
D)
E)

Question 36

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 37

Add the rational expressions. Be sure to express your answer in simplest form.

A)
B)
C)
D)
E)

Question 38

Perform the operation and simplify the result when possible.

A)
B)
C)
D)
E)

Question 39

Perform the operation and simplify the result when possible.

A)
B)
C)
D)
E)

Question 40

Add the rational expressions. Be sure to express your answer in simplest form.

A)
B)
C)
D)
E)

Question 41

Perform the division.

A)
B)
C)
D)
E)

Question 42

Perform the division: by .

A)
B)
C)
D)

Question 43

A board 5 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board. __________ feet

Question 44

The focal length f of a lens is given by the formula where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

Question 45

Solve the equation and check the solution.

A) - 2
B) 4
C) 3
D) - 3
E) no solution

Question 46

Perform the division: by .

A) x + 2
B) x - 2
C) x + 5
D) x + 1

Question 47

Solve the equation and check the solution.

A) - 16
B) - 8
C) 16
D) 8
E) no solution

Question 48

Perform the division: by .

Question 49

Perform the division: by .

Question 50

Perform the division. Write the answer without using negative exponents.

A)
B)
C)
D)

Question 51

Solve for c .

A)
B)
C)
D)

Question 52

Perform the division. Write the answer without using negative exponents.

A)
B)
C)
D)

Question 53

Solve the equation and check the solution.

A) - 20
B) - 10
C) 20
D) 10
E) no solution

Question 54

Suppose that the width of a certain rectangle is 3 inches more than one-fourth of its length. The perimeter of the rectangle is 66 inches. Find the length and width of the rectangle. length: __________ inches width: __________ inches

Question 55

Solve the formula for t :

Question 56

Perform the division: by .

Question 57

Perform the division.

A)
B)
C)
D)
E)

Question 58

Perform the division. Write the answer without using negative exponents.

A)
B)
C)
D)

Question 59

Perform the division.

A)
B)
C)
D)
E)

Question 60

Use an algebraic approach to solve the problem. If the complement of an angle is 9^o less than one-fourth of its supplement, find the measure of the angle.

A) 72^o
B) 70^o
C) 60^o
D) 66^o
E) 64^o

Question 61

Find f ( c ) by evaluating directly and by using synthetic division and the remainder theorem. f ( x ) = x ² + 2 x + 4 and c = 9

A) 95
B) 9
C) 107
D) 99
E) 103

Question 62

Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. a = 13, b = 4, c = 34

A) ft
B) ft
C)
D)

Question 63

Use synthetic division to perform the division.

A) x + 6
B) x + 9
C) x - 9
D) x - 8
E) x - 6

Question 64

If P ( y ) is a polynomial in y , then P ( r ) = 0 if and only if __________ is a factor of P ( y ).

A) -r - y
B) y + r
C) y - r
D) r - y

Question 65

Use synthetic division to perform the division.

Question 66

A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,750 students?

A) 190 teachers
B) 176 teachers
C) 165 teachers
D) 181 teachers
E) 222 teachers

Question 67

A model railroad engine is 2 inches long. If the scale is 168 feet to 1 foot, how long is the real engine?

A) 31
B) 29
C) 26
D) 34
E) 28

Question 68

Use the factor theorem and tell whether the first expression is a factor of P ( x ). x + 1; P ( x ) = x ³ + 3 x ² - 3 x - 5 . (Hint: Write x + 1 as x - (-1).)

A) yes
B) no

Question 69

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

A) h = 27 ft
B) h = 42 ft
C) h = 30 ft
D) h = 35 ft
E) h = 22 ft

Question 70

Perform the division: by .

Question 71

Use a calculator and synthetic division to perform the division.

A)
B)
C)
D)

Question 72

Solve the proportion for the variable. z = __________

Question 73

Express the sentence as a formula. Assume that is a constant of variation. The distance that a body falls varies directly with the square of the time .

A)
B)
C)
D)
E)

Question 74

Assume that all variables represent positive numbers. Assume that varies directly with . If when , find when .

A)
B)
C)
D)
E)

Question 75

Use the factor theorem and tell whether the first expression is a factor of P ( x ). x ; P ( x ) = 7 x ³ - 7 x ² - 8 x . Hint : Write x as x - 0.

A) no
B) yes

Question 76

Let P ( x ) = 4 x ³ - 3 x ² + 2 x - 5. Evaluate P ( x ) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. P (-4)

A) P (-4) = -327
B) P (-4) = -317
C) P (-4) = -322
D) P (-4) = -347

Question 77

Solve the proportion for the variable. y = __________

Question 78

Solve for the variable in the proportion.

A)
B)
C)
D)
E)

Question 79

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer.

A) x = 870 ft
B) x = 813 ft
C) x = 845 ft
D) x = 885 ft
E) x = 833 ft

Question 80

A recipe for spaghetti sauce requires 6 bottles of ketchup to make 8 gallons of sauce. How many bottles of ketchup are needed to make 56 gallons of sauce?