The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 6.9: ADDING AND SUBTRACTING ALGEBRAIC

FRACTIONS WITH UNLIKE DENOMINATORS

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Follow the steps below to add or subtract algebraic fractions with unlike denominators.

Assume that the denominators of the fractions are not equal to zero.

1. Find the least common denominator (select the largest exponent of every factor).


2. Write equivalent fractions.


3. Add or subtract.


4. Simplify, if possible.

EXAMPLE

2

x+ 3

−

1

x+ 1

The least common denominator is (x+ 3 )(x+ 1 ) because the factors are (x+ 3 )and(x+ 1 ).

The largest exponent of each factor is 1.

Write equivalent fractions and subtract.

2

x+ 3

·

x+ 1

x+ 1

−

1

x+ 1

·

x+ 3

x+ 3

=

2 x+ 2 −x− 3

(x+1)(x+3)

=

x− 1

(x+1)(x+3)

This fraction cannot be simplified.

DIRECTIONS: Find each sum or difference.

1.

x

4

+

2 x

9

2. 
   

1

x+ 1

−

1

x

3. 
   

2

x

+

3

x^2

4. 
   

6

x+ 3

−

2

x− 3

5.

3 x− 2

6

−

x− 3

9

CHALLENGE:Shawn found the sum of

3

x+ 1

and

5

(x+1)^2

. He added the

numerators and found the sum to be

8

(x+1)^2

. Do you agree with his
answer? Explain your reasoning.

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Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.