Name ________________________________________ Date __________________ Class__________________
LESSON
5-2
Reading Strategy
Follow a Procedure
Dividing rational expressions can be thought of as multiplying by the
reciprocal of the divisor. In order to divide a rational expression, rewrite the
division as multiplication, simplify, and multiply.
STEP 1
5 x 2 10 x

3y
6y 2
STEP 2
5x 2 3y

6 y 2 10 x
x 1

2y 2
Multiply by the reciprocal
of the divisor.
Simplify by dividing out
common factors.
STEP 3
x
4y
Multiply.
Answer each question.
1. For
8x
,
8 x  16
a. Simplify the expression.
____________________
b. For which value of x is the expression undefined?
____________________
c. Explain why the expression is undefined for this value.
____________________________________________________________________________________
2. For the expression
6 x 3 y 2 2 xy 2

7z 4
21z 2
a. Rewrite as multiplication.
________________________
b. Simplify.
c. Multiply.
_________________________
________________________
d. For which value is the resulting expression undefined?
____________________
3. For the expression
3( x  1) 9( x  1)

2( x  2) 4( x  2)
a. Rewrite as multiplication.
________________________
b. Simplify.
c. Multiply.
_________________________
________________________
d. For which value is the resulting expression undefined?
4. Explain how to check the results of division.
________________________
____________________________________________________________________________________
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5-18
Holt McDougal Algebra 2
b.
T3
= 1.067
T2
5.
6x + 8
x−4
6.
c.
T3
= 1.143
T1
7.
4x + 3
x − 3x − 4
8.
−x + 2
x2 − 1
9.
x2
6
10.
2
x + 5x
12.
5x
x + 4x + 3
4. D
5. A
Reading Strategies
1. a.
x
x−2
11. 1
b. x = 2
13. 54.5 miles per hour
c. Because x = 2 makes the
denominator of the expression equal
to 0
Practice B
2
2
1. 15x3y6
2. (x − 1)(x + 2)(x − 3)
6 x 3 y 2 21z 2
⋅
7z 4
2 xy 2
3.
b.
3x 2 3
⋅
z2 1
6x − 8
; x ≠ −4
x+4
4.
c.
9x 2
z2
−2 x + 14
5
;x ≠
2x − 5
2
5.
2x 2 + 7 x + 4
; x ≠ 4, x ≠ −3
x 2 − x − 12
6.
2x 2 − 5 x − 7
; x ≠ 6, x ≠ −3
x 2 − 3 x − 18
2. a.
d. z = 0
3( x − 1) 4( x + 2)
3. a.
⋅
2( x + 2) 9( x − 1)
b.
1 2
⋅
1 3
7.
x 2 − 4x + 2
; x ≠ −3, x ≠ 5
x 2 − 2 x − 15
c.
2
3
8.
−2 x 2 − 3 x + 6
; x ≠ −2, x ≠ 9
x 2 − 7 x − 18
d. The resulting expression is never
undefined.
9.
4. By multiplying the result by the divisor;
if it is correct their product should be
the dividend.
RATIONAL EXPRESSIONS
Practice C
Practice A
3x
; x ≠ −1
x +1
3. 12x2
2.
x 2 − 4x + 3
10.
x 2 + 11x + 30
12 x − 24
3
x + 3x 2 + x + 3
11. 2.6 6 packages per hour
5-3 ADDING AND SUBTRACTING
1.
2
−2 x 2 + 6 x + 12
x 2 + 2x
−2 x + 1
5
;x ≠
2x − 5
2
4. (x + 1)(x + 2)
1.
13 x − 2
; x ≠ −3
2x + 6
2.
x 2 + 28 x
; x ≠ −4, x ≠ 0
3x 2 ( x + 4)
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A57
Holt McDougal Algebra 2