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

Name Date

WORKSHEET 6.8: WRITING EQUIVALENT ALGEBRAIC

FRACTIONS

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Use the steps below to write equivalent algebraic fractions. Assume that the denominators of

the fractions are not equal to zero.

1. Factor the denominators.


2. Multiply the fraction by 1.

EXAMPLE

x

x+ 1

=

x^2 + 3 x+ 2

x+ 1 cannot be factored. The factors ofx^2 + 3 x+ 2 arex+ 1 andx+ 2.

Multiply by 1, expressed as

x+ 2

x+ 2

.

x

x+ 1

·

x+ 2

x+ 2

=

x^2 +^2 x

x^2 + 3 x+ 2

DIRECTIONS: Write equivalent fractions.

3

x

=

x^2 + 2 x

1

x+ 5

=

x^2 + 8 x+ 15

5

x− 2

=

x^2 − 7 x+ 10

2

x+ 7

=

x^2 + 8 x+ 7

5.

x^2

x− 2

=

x^2 −x− 2

6.

x+ 4

x+ 2

=

x^2 + 5 x+ 6

CHALLENGE:Just by looking at the problem, Samantha said that the

numerator of a fraction equivalent to

x+ 2

x+ 2

=

x^2 + 6 x+ 4

isx^2 + 6 x+4.

Explain how she could have arrived at this conclusion.

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©

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