Beginning Algebra, 11th Edition

Multiply.

Combine like terms.

The numerator cannot be factored here, so the expression is in lowest terms.

NOW TRY

NOTE If the final expression in Example 4could be written in lower terms, the

numerator would have a factor of or Therefore, it is only

necessary to check for possible factored forms of the numerator that would contain

one of these binomials.

Adding Rational Expressions (Denominators Are Opposites)

Add. Write the answer in lowest terms.

The denominators are opposites. Use the process of multiplying one of the frac-

tions by 1 in the form to get the same denominator for both fractions.

Multiply by.

Distributive property

Rewrite as

Add numerators.

Keep the same denominator.

If we had chosen as the common denominator, the final answer would be

, which is equivalent to NOW TRY

OBJECTIVE 3 Subtract rational expressions.

y- 8

y- 2.

8 - y

2 - y

2 - y

=

y- 8

y- 2

= - 2 +y y-2.

y

y- 2

+

- 8

y- 2

=

y

y- 2

+

- 8

• 2 +y
  
  
  • 1
  
  
  • 1
  
  
  
  

8

= 2 - y

y

y- 2

+

81 - 12

12 - y 21 - 12

• 1


• 1

y

y- 2

+

8

2 - y

EXAMPLE 5

x+2,x+3, x-1.

=

3 x^2 +x+ 2

1 x+ 221 x+ 321 x- 12

=

2 x^2 - 2 x+x^2 + 3 x+ 2

1 x+ 221 x+ 321 x- 12

SECTION 7.4 Adding and Subtracting Rational Expressions 443

Add numerators.

= Keep the same denominator.

2 x 1 x- 12 + 1 x+ 121 x+ 22

1 x+ 221 x+ 321 x- 12

NOW TRY
EXERCISE 4
Add. Write the answer in
lowest terms.

x- 1

x^2 + 6 x+ 8

+

4 x

x^2 +x- 12

Subtracting Rational Expressions (Same Denominator)

The rational expressions and are subtracted as follows.

That is, to subtract rational expressions with the same denominator, subtract the

numerators and keep the same denominator.

P

Q



R

Q



PR

Q

QP RQ^1 QZ^02

NOW TRY
EXERCISE 5
Add. Write the answer in
lowest terms.

2 k

k- 7

+

5

7 - k

NOW TRY ANSWERS

4. 
   

5.^2 k-^5
k- 7
, or 5 -^2 k
7 - k

5 x^2 + 4 x+ 3

1 x+ 421 x+ 221 x- 32