Beginning Algebra, 11th Edition

OBJECTIVE 2 Write equivalent rational expressions.Once the LCD has

been found, the next step in preparing to add or subtract two rational expressions is to

use the fundamental property to write equivalent rational expressions.

SECTION 7.3 Least Common Denominators 437

Writing Equivalent Rational Expressions

Rewrite each rational expression with the indicated denominator.

(a) (b)

Step 1 For each example, first factor the denominator on the right. Then compare

the denominator on the left with the one on the right to decide what factors

are missing. (It may sometimes be necessary to factor both denominators.)

Step 2 A factor of 5 is missing. Factors of 2 and kare missing.

Step 3 Multiply by Multiply by

NOW TRY

Writing Equivalent Rational Expressions

Rewrite each rational expression with the indicated denominator.

(a)

Factor the denominator on the right.

The missing factor is 4, so multiply the fraction on the left by

Fundamental property

8

3 x+ 1

#^4

4

=

32

12 x+ 4

4

4.

8

3 x+ 1

=

?

413 x+ 12

8

3 x+ 1

=

?

12 x+ 4

EXAMPLE 5

2 k

2 k

= 1

5

5

= 1

9 k

25

=

9 k

25

#^2 k

2 k

=

18 k^2

50 k

3

8

=

3

8

#^5

5

=

15

40

2 k

2 k^.

9 k

25

5

5.

3

8

9 k

25

=

?

25 # 2 k

3

8

=

?

5 # 8

9 k

25

=

?

50 k

3

8

=

?

40

NOW TRY EXAMPLE 4
EXERCISE 4
Rewrite each rational expres-
sion with the indicated
denominator.

(a) (b)
4 t
11

=

?

33 t

2

9

=

?

27

NOW TRY ANSWERS

4. (a) (b)
   12 t^2
   33 t

6

27

Writing a Rational Expression with a Specified Denominator

Step 1 Factorboth denominators.

Step 2 Decide what factor(s) the denominator must be multiplied byin

order to equal the specified denominator.

Step 3 Multiplythe rational expression by that factor divided by itself.

(That is, multiply by 1.)