Name ________________________________________ Date __________________ Class __________________
LESSON
9-2
Multiplying and Dividing Rational Expressions
Practice and Problem Solving: Modified
Multiply. State any excluded values. The first one is done for you.
1.
4 2x 2
i
7
5
2.
8x 2
; None
35
________________________________________
3.
________________________________________
6 ( x − 7)
x+6
i
x − 4 ( x − 7 )( x + 6 )
4.
________________________________________
5.
6
5
i
2
6
5x
( x + 5 )( x − 1)
3
i
6 ( x + 2)
( x − 1)( x + 2)
________________________________________
x2 − 4
2x + 2
i
2
x −x −2 x +2
6.
________________________________________
5
x 2 + 3 x − 18
i
x 2 + 3 x − 18 2 x 3 − 16 x 2
________________________________________
Divide. State any excluded values. The first one is done for you.
7.
3x 2
2
÷ 5
5
2x
8.
3x 7
; x =0
5
________________________________________
9.
________________________________________
1
2
÷ 3
2
2x
2 x − 10 x 2
10.
________________________________________
11.
12.
________________________________________
13. A rectangular sandbox has a length of
x+2
1
÷ 2
x + 1 x + 3x + 2
________________________________________
3 x 2 − 12 x
x+5
÷ 2
2
3 x + 15 x x + 10 x + 25
Solve.
( x + 2 )( x + 1) ÷ x + 5
2 ( x + 1)
2
6x + 6
8x + 8
÷ 3
3
2
4x − 8x
4x − 8x 2
________________________________________
3 x + 24
feet and a width of
x+2
x +9
feet. Write a rational expression that represents the area of
2 x + 16
the sandbox. Simplify the expression and state any excluded values.
_______________________________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
166
Name ________________________________________ Date __________________ Class __________________
LESSON
9-2
Multiplying and Dividing Rational Expressions
Practice and Problem Solving: A/B
Multiply. State any excluded values.
1.
6x 6x
i
10 3 x 3
2.
________________________________________
3.
________________________________________
1
7 x 3 + 49 x 2
i
x+9
x +7
4.
________________________________________
5.
4x 8x
i
3
2
6 x 2 − 54 x 7 x
i
6x
x −9
________________________________________
18 x − 36
2
i
4x − 8
9 x + 18
(
)
6. 56 + 11x − 15 x 2 i
________________________________________
10
15 x − 11x − 56
2
________________________________________
Divide. State any excluded values.
7.
4x 4x
÷
5x
6
8.
________________________________________
9. ( 2 x + 6 ) ÷
( x − 1)( x − 10 )
÷
x −2
x − 10
________________________________________
14 x 2 + 42 x
10
10.
________________________________________
11.
6 ( x − 2)
27 x + 9 3 x 2 − 8 x − 3
÷
10
10
________________________________________
24 x + 56
15 x + 35
÷
3
2
10 x − 90 x
5
12.
________________________________________
2 x + 20
2
÷
3
2
12 x − 30 x
14 x − 35
________________________________________
Solve.
13. The distance, d, traveled by a car undergoing constant acceleration, a,
1
for a time, t, is given by d = v 0 t + at 2 , where v 0 is the initial velocity of
2
the car. Two cars are side by side with the same initial velocity. One
car accelerates, a = A, and the other car does not accelerate, a = 0.
Write an expression for the ratio of the distance traveled by the
accelerating car to the distance traveled by the nonaccelerating car as
a function of time.
_________________________________________________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
164