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

Name Date

WORKSHEET 6.6: ADDING AND SUBTRACTING ALGEBRAIC

FRACTIONS WITH LIKE DENOMINATORS

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Follow the steps below to add and subtract algebraic fractions with like denominators.

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

1. Add or subtract the numerators. If you are subtracting, add the opposite of each term in
   the numerator of the second fraction.


2. Place the sum or difference over the denominator.


3. Factor the numerator and the denominator, if possible.


4. Use the cancellation rule to simplify.

EXAMPLES

x

x^2 + 3 x+ 2

+

2

x^2 + 3 x+ 2

=

x+ 2

x^2 + 3 x+ 2

=

x+ 2

(x+2)(x+1)

=

1

x+ 1

x^2

x^2 − 4 x+ 5

−

2 x+ 3

x^2 − 4 x+ 5

=

x^2 − 2 x− 3

x^2 − 4 x− 5

=

(x−3)(x+1)

(x−5)(x+1)

=

x− 3

x− 5

DIRECTIONS: Find the sum or difference. Simplify.

1.

x^2

x+ 1

−

1

x+ 1

2.

3 x

6 x+ 8

+

4

6 x+ 8

3.

x

x^2 −x− 20

−

5

x^2 −x− 20

4.

x^2

x^2 − 3 x+ 2

+

3 x− 4

x^2 − 3 x+ 2

5.

x^2 + 8 x

x^2 + 10 x+ 25

+

15

x^2 + 10 x+ 25

6.

x^2

x^2 − 2 x+ 1

−

6 x− 5

x^2 − 2 x+ 1

CHALLENGE:Julian said that

x^2

x^2 +x− 2

−

7 x+ 6

x^2 +x− 2

=

x^2 − 7 x+ 6

x^2 +x− 2

.He

simplified his answer as

x− 6

x+ 2

. Is he correct? Explain your answer.

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Copyright

©

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