Name _______________________________________ Date ___________________ Class __________________
CHAPTER
8
Chapter Review
Form A
1. Simplify
6 x  18 x 2  5 x  6

.
x2  4
x2  9
A
6
x2
B
6 x  12
x2  x  6
2. Find the solution set for the equation
x 2  6x  8
5.
x2
A {9}
B {2, 9}
3. Simplify
1
x
.

1 x x  1
A 1
x 1
B
x 1
x 1
C 1 x
x 1
D
 x  1
2
4. Which of the following is equal to
x
1
x 1
A
x
B
x
x 1
1
x
?
x 1
2
C x
D
x2
x 1
5. Ted walks from his home to the post office at an average rate of 3 miles per hour. He then
walks back at an average rate of 5 miles per hour. What is his average rate for the entire
trip?
A 3.6 mph
C 4 mph
B 3.75 mph
D 4.3 mph
Name _______________________________________ Date ___________________ Class __________________
Chapter Review
CHAPTER
8
Form A continued
6. How many solutions are there to the equation
A
B
C
D
2
4
 2
 1?
x 1 x 1
0
1
2
an infinite number
7. Working alone, Machine A can produce 1000 widgets in 6 hours. Working alone, Machine B
can produce 1000 widgets in 9 hours. How long will it take the two machines to produce the
1000 widgets if they are both used at the same time?
A 3 hours and 36 minutes
B 3 hours and 45 minutes
8. Which expression is equal to
1
xy 3
?
xy
1
A x 2 y2
3
5
B x2y 2
9. Which is equal to 10?
A
B


10. Solve

10  
10
3
4

10  
10
6
8

10 
10
5x  2  2 2x  5 .
A x  8
B x6
11. Which is an extraneous solution to
3x  1  x  3 ?
A x1
B x5
C x8
D There is no extraneous solution.
12. What is the solution set to the equation
1
x  3   5 x  1 2 ?
A {10}
Name _______________________________________ Date ___________________ Class __________________
B {1, 10}
Name _______________________________________ Date ___________________ Class __________________
CHAPTER
8
Chapter Review
Form B
Select the best answer.
1. Simplify
F
x 2  3 x  10
x2  x  6

.
x 2  2 x  15 x 2  6 x  9
x5
x 5
x 2  8 x  15
2
H x  7 x  10
 x  2  x  5
2
 x  3  x  5
2
G
x3
x 3
J
2. Find the solution set for the equation
3x
 3 .
x2  9
 10 
A  
 3
 8
B  
 3
3. Simplify
F
G
8 
C  
3 
10 
D  
3
1
x
 2
.
1 x x  1
1
x 1
2
1
x2  1
H
2x  1
x2  x
x 1
x  x2  x  1
2
J
1
x ?
4. Which of the following is equal to
1
1
x
x 1
x2  1
A
C
x 1
x
1
B
x 1
x 1
D
x2  1
x2
5. Ted walks from his home to the post office at an average rate of 3 miles per hour. He then
runs back at an average rate of 7 miles per hour. What is his average rate for the entire
trip?
F 4.2 mph
H 5 mph
G 4.6 mph
J 5.3 mph
Name _______________________________________ Date ___________________ Class __________________
CHAPTER
8
Chapter Review
Form B continued
6. What is the sum of all the solutions of the equation
A 
1
3
2
4

9?
x x 1
1
3
D 1
C
B 0
7. Working alone, Eric can paint a room in 9 hours. Eric and Matt working together can paint
the room in 4 hours. How long will it take Matt to paint the room working alone?
F 6 hours and 30 minutes
G 7 hours
H 7 hours and 12 minutes
J 7 hours and 20 minutes
8. Which expression is equal to
xy 3
4
x3y
?
5
y4
5
1
3
4
C x
A x4y 4
B
1
5 7
x4y 4
9. Solve
5
4 4
D x y
3 x  3  6 x  10 .
F 11
G 16
H 21
J no solution
10. Which is an extraneous solution to
6 x  1  2x  3 ?
A x  4
1
B x
2
C x4
D There is no extraneous solution.
11. What is the solution set to the equation
1
x  2  3x  4 2 ?
F {3}
H {7}
G {0, 3}
J {0, 7}
Name _______________________________________ Date ___________________ Class __________________
CHAPTER
8
Chapter Review
Form C
1. Simplify
x 2  16
5 x  10

.
2
x  6 x  8 3 x  12
2. Find the solution set for the equation
3. Simplify
4. Simplify
4 x 2  25
 14 .
2x  5
2
3

.
x  3 x 2  7 x  12
x2
.
4
x
x
5. Carol drives her daughter to school at an average rate of 30 miles per hour, but only goes
an average rate of 20 miles per hour on the way home because of traffic. What is her
average rate for the entire round trip?
6. Find the solution set for the equation
3
10

 1.
x  1 x 2  2x  1
Name _______________________________________ Date ___________________ Class __________________
CHAPTER
8
Chapter Review
Form C continued
7. Pipe A can fill a pool in 8 hours. Pipe B can fill the pool in 4 hours. How long will it take
Pipes A and B to fill the pool if they are both used?

8. Simplify

9. Simplify
 4  4 .
10. Solve
xy 3
3
3
x2y
 and express with rational exponents.
6
6 x  5  41  2 x .
11. Find the solution set to
3 x  3  2x  5 .
1
12. Solve the equation 2x  4   6  2x  2 .
Name _______________________________________ Date ___________________ Class __________________
CHAPTER
8
Chapter Review
Form D
1. Simplify
x 2  9 x  36 2 x 2  21x  36

.
x 2  3 x  18 2 x 2  15 x  18
2. Find the solution set for the equation
3. Simplify
x2 2
 .
x2  4 3
1
x 1
.
 2
2x x 4
1
x.
4. Simplify
1
x
x
x
5. Emmett runs once around the school track at an average rate of 8 miles per hour. Then he
jogs once around the track at an average rate of 6 miles per hour. What is his average rate
for the two laps of the track?
Name _______________________________________ Date ___________________ Class __________________
CHAPTER
8
Chapter Review
Form D continued
6. Find the solution set for the equation
2
6

 15 .
x x 1
7. Inlet pipe #1 can fill a pool in 8 hours. Inlet pipes #1 and #2 together can fill the pool in 6
hours. How long will it take inlet pipe #2 to fill the pool by itself?
8. Simplify
9. Simplify
10. Solve
xy 3 3 x 2 y
and express with rational exponents.
xy
 8  8 .
6
8x  3  2 7x  3 .
11. Find the solution set to
6 x  5  2x  3 .
1
12. Solve the equation x  5   4x  1 2 .