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

Name Date

WORKSHEET 6.4: IDENTIFYING RESTRICTIONS ON THE

VARIABLE

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A restriction on a variable in the denominator of a fraction is a value that the variable may not

equal. Otherwise the fraction will have no meaning. Follow the steps below to identify

restrictions on a variable:

1. If the highest degree of the variable in the denominator is 1, write an inequality, stating
   that the denominator cannot equal 0.


2. If the degree of the variable in the denominator is 2 or more, factor the denominator
   and write an inequality, stating that each factor cannot equal 0.


3. Solve each inequality to find the restrictions on the variable.

EXAMPLES

Find restrictions on the variables below.

3

x+ 1

Because the exponent ofxis 1, write and solve the inequality: x+ 1 = 0 ;x=− 1.

4

x^2 − 6 x+ 5

Factorx^2 − 6 x+ 5 : x^2 − 6 x+ 5 =(x−5)(x−1). Write the inequalities:

x− 5 = 0 andx− 1 = 0. Solve each inequality:x= 5 andx= 1.

DIRECTIONS: Find the restrictions on the variable.

3

x− 4

2.

2 x

4 x

3.

x− 1

x^2 − 1

4.

5 x^2

x^2 + 3 x− 4

5.

x^2 − 4

x^2 − 10 x− 11

1

x^2 + 6 x− 7

8

x^2 −x

8.

x^2 + 3 x

x^2 + 13 x+ 40

CHALLENGE:Marty said

x− 2

x− 2

=1. Do you agree? Explain your answer.

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