Multiplying Rational Expressions

Multiply. Write the answer in lowest terms.

Multiply numerators.

Multiply denominators.

Factor. Identify the common factors.

=^1 xx 1 x++y^2 y^ x 2 = 1 ; Write in lowest terms.

x

21 x+y 2

=

1 x+y 2 x#x

2 x 1 x+y 21 x+y 2

=

1 x+y 2 x^2

2 x 1 x+y 22

x+y

2 x

x

2

1 x+y 22

EXAMPLE 2

430 CHAPTER 7 Rational Expressions and Applications

So, to divide by we multiply by the reciprocal of namely, 4. Since

there are or^72 , 321 , qtin 87 gal.

7

8142 =

7

2 ,

1

4 ,

7

8

1

4 ,

7

8

Let and.

AKis the reciprocal of Q=^14 .B

P= 87 ,Q=^14 , K= 4

Use parentheses

here around

x+y.

NOW TRY
EXERCISE 2
Multiply. Write the answer in
lowest terms.

m- 3

3 m

#^9 m

2

81 m- 322

NOW TRY ANSWERS

2. 81 m^3 m- 32

NOW TRY
EXERCISE 3
Multiply. Write the answer in
lowest terms.

y^2 - 3 y- 28

y^2 - 9 y+ 14

y

(^2) - 7 y+ 10
y^2 + 4 y
3.y-y^5
NOW TRY
Multiplying Rational Expressions
Multiply. Write the answer in lowest terms.
Definition of multiplication
Factor.
Divide out the common factors.
The quotients and all equal 1, justifying the final product
NOW TRY
OBJECTIVE 2 Divide rational expressions. Suppose we have of milk
and want to find how many quarts we have. Since 1 qt is we ask, “How many
are there in ” This would be interpreted as follows.
or The fraction bar means division.
The fundamental property of rational expressions discussed earlier can be applied
to rational number values of P, Q, and K.

=

7

8

#^4

1

7

8

4

1

=

7

8

4

1

4

4

P

Q

=

P#K

Q#K

=

7

8

1

4

7

8

,

1

4

,

7

8?

1

4 s

1

4 gal,

7

8 gal

x

x+ 1.

x- 1

x- 1

x- 4

x- 4 ,

x+ 3

x+ 3 ,

=

x

x+ 1

=

x 1 x+ 321 x- 421 x- 12

1 x- 421 x+ 121 x+ 321 x- 12

=

1 x^2 + 3 x 21 x^2 - 5 x+ 42

1 x^2 - 3 x- 421 x^2 + 2 x- 32

x^2 + 3 x

x^2 - 3 x- 4

#x

(^2) - 5 x+ 4
x^2 + 2 x- 3
EXAMPLE 3
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