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