is equivalent to multiplying the numerator and denominator of the
original expression by 6.
Creating Equivalent Rational Expressions
Convert each expression to an equivalent rational expression with the indicated
denominator.
a.
b.
w
w
5
w
2
3
w
10
7
5
p
2
20
p
6
Example 3
6
6
1
2
6
6
1
2
1
2
1
2
6
6
1
6
2
6
6
12
1
2
p
q
p
q
1
p
q
r
r
pr
qr
r
0,
q
0
6
z
7
;
1
7
z
6
x
2
5
x
6
5
x
2
4
;
1
2
x
6
;
1
9
a
3
b
2
;
5
18
a
4
b
7
40
;
1
15
;
5
6
Skill Practice
1
x
3
2
.
1
3
x
2
x
3
3
x
3
x
x
3
LCD
1
1
21
3
x
2
LCD
1
x
3
21
1
2
x
4
1
1
x
3
2
;
1
3
x
x
4
x
3
;
1
1
1
3
x
2
If
1
x
3 and 3
x
x
4
x
3
;
1
3
x
424
Chapter 6
Rational Expressions and Rational Equations
Skill Practice Answers
4.
120
5.
6.
2(
x
2)(
x
2)(
x
3)
7.
z
7 or 7
z
18
a
4
b
2

Section 6.3
Addition and Subtraction of Rational Expressions
425
Solution:
a.
can be written as
.
Multiply the numerator and denominator by
the missing factor,
b.
Factor the denominator.
Multiply the numerator and denominator by the
missing factor
Fill in the blank to make an equivalent fraction with the given
denominator.
8.
9.
5
b
b
3
b
2
9
1
8
xy
16
x
3
y
2
Skill Practice
w
2
2
w
1
w
5
21
w
2
2
1
w
2
2
.
w
w
5
w
w
5
w
2
w
2
1
w
5
21
w
2
2
w
w
5
w
2
3
w
10
28
p
4
20
p
6
4
p
4
.
7
5
p
2
7
5
p
2
4
p
4
4
p
4
5
p
2
4
p
4
20
p
6
5
p
2
4
p
4
7
5
p
2
20
p
6
4. Addition and Subtraction of Rational Expressions
with Unlike Denominators
To add or subtract rational expressions with unlike denominators, we must con-
vert each expression to an equivalent expression with the same denominator.
For example,
consider adding the expressions
. The LCD is
For each expression, identify the factors from the LCD that are
missing in the denominator. Then multiply the numerator and denominator of
the expression by the missing factor(s):
The rational expressions now
have the same denominator
and can be added.
1
3
2
1
x
2
2
1
x
1
2
1
x
1
2
1
5
2
1
x
1
2
1
x
2
2
1
x
2
2
1
x
2
21
x
1
2
.
3
x
2
5
x
1
TIP:
In the final answer in Example 3(b) we multiplied the polynomials in the
numerator but left the denominator in factored form. This convention is followed
because when we add and subtract rational expressions, the terms in the
numerators must be combined.
Skill Practice Answers
8.
9.
5
b
2
15
b
2
x
2
y

426
Chapter 6
Rational Expressions and Rational Equations
Combine terms in the numerator.
Clear parentheses and simplify.
8
x
7
1
x
2
21
x
1
2
3
x
3
5
x
10
1
x
2
21
x
1
2
3
1
x
1
2
5
1
x
2
2
1
x
2
21
x
1
2
Steps to Add or Subtract Rational Expressions
1.
Factor the denominator of each rational expression.
2.
Identify the LCD.
3.
Rewrite each rational expression as an equivalent expression with the
LCD as its denominator.
4.
Add or subtract the numerators, and write the result over the common
denominator.
5.
Simplify if possible.
Adding and Subtracting Rational Expressions
with Unlike Denominators
Add or subtract as indicated.

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