Beginning Algebra, 11th Edition

Writing in Lowest Terms

Write each rational expression in lowest terms.

(a)

Factor. (Step 1)

= Fundamental property (Step 2)

3

5

=

31 x- 42

51 x- 42

3 x- 12

5 x- 20

EXAMPLE 4

We use the fundamental property of rational expressionsto write a rational

expression in lowest terms.

422 CHAPTER 7 Rational Expressions and Applications

Fundamental Property of Rational Expressions

If is a rational expression and if Krepresents any polynomial, where

then the following is true.

PK

QK



P

Q

KZ0,

QP^1 Q Z^02

This property is based on the identity property of multiplication.

Writing in Lowest Terms

Write each rational expression in lowest terms.

EXAMPLE 3

PK

QK

=

P

Q

#K

K

=

P

Q

# 1 = P

Q

(b)

Write as and as

14 k^2

2 k^3

=

2 # 7 #k#k

2 #k#k#k

k^2 k#k k^3 k#k#k.

14 k^2

2 k^3

(a)

Begin by factoring.

30

72

=

2 # 3 # 5

2 # 2 # 2 # 3 # 3

30

72

Group any factors common to the numerator and denominator.

Use the fundamental property.

NOW TRY

14 k^2

2 k^3

=

7

k

30

72

=

5

2 # 2 # 3

=

5

12

14 k^2

2 k^3

=

712 #k#k 2

k 12 #k#k 2

30

72

=

5 # 12 # 32

2 # 2 # 3 # 12 # 32

since the

denominator is 0

for this value.

xZ4,

The given expression is equal to for all values of x, where (since the denom-

inator of the original rational expression is 0 when xis 4).

(^35) xZ 4
NOW TRY
EXERCISE 3
Write the rational expression
in lowest terms.
21 y^5
7 y^2
NOW TRY ANSWER

3. 3 y^3

Writing a Rational Expression in Lowest Terms

Step 1 Factorthe numerator and denominator completely.

Step 2 Use the fundamental propertyto divide out any common factors.

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