Beginning Algebra, 11th Edition

(Marvins-Underground-K-12) #1
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



  1. 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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