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

Name Date

WORKSHEET 6.10: MULTIPLYING AND DIVIDING ALGEBRAIC

FRACTIONS

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Follow the steps below to multiply and divide algebraic fractions. Assume that the

denominators of the fractions are not equal to zero.

1. For division problems, rewrite the problem as multiplication by using the reciprocal of
   the fraction immediately following the division symbol.


2. Factor the numerators and denominators.


3. Cross out the common factors (if there are any) in the numerators with the same com-
   mon factors in the denominators.


4. Express your answer in factored form.

EXAMPLE

x+ 4 x+ 1

x+ 3 (x+ 3)(x + 1)

x+ 4

==

x^2 + 4 x+ 3

x+ 1

x+ 3

x+ 4

(x+ 3)^2

··

DIRECTIONS: Multiply or divide. Express your answers in factored form.

2 x+ 4

x+ 3

·

x^2 +^7 x+^12

x+ 2

2.

x+ 3

x^2 − 9

÷

x+ 3

x− 3

3.

3 x

5

·

x+ 4

6 x+ 6

4.

3 x^2

4

÷

6 x+ 9

2

5.

2 x^2 + 3 x+ 1

x^2 − 4

÷

x^2 − 1

x+ 2

6.

x^2 −x− 12

x− 2

·

x− 3

x^2 +x− 6

CHALLENGE:Sienna said that

x^2 − 4

x^2 − 16

÷

x+ 2

x− 2

=

(x+2)^2

(x−4)(x+4)

. Her teacher

said that her answer was wrong. Find Sienna’s error and correct her work.

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Copyright

©

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