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

Name Date

WORKSHEET 6.13: SOLVING FRACTIONAL EQUATIONS

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Use the steps that follow to solve fractional equations:

1. Multiply both sides of the equation by the least common denominator (LCD) to obtain
   an equivalent equation that has no fractions.


2. Follow the steps for solving equations to find your solution.


3. Check the original problem to see if there are any restrictions on the variable. (Remem-
   ber, the denominator of a fraction cannot equal 0.) Modify your solution, if necessary.

EXAMPLE

Solve forx.

4 x− 4

x− 1

− 4 = 0

x− 1

[

4 x− 4

x− 1

− 4 = 0

]

→ 4 x− 4 −4(x−1)= 0 → 4 x− 4 − 4 x+ 4 = 0 → 0 = 0

Although 0=0 is true for all real numbers, the solution to the original equation is all real

numbers except 1 because the denominator cannot equal 0.

DIRECTIONS: Solve and check. If there is no solution, write ‘‘no solution.’’

3

4 n

+

1

2 n

=

5

8

2

x

+

x

x+ 3

= 1 3.

2 y− 5

8 y− 5

−

1

4

= 0

3 y− 6

y− 2

= 3 5.

3

x

−

1

4

=

1

12

CHALLENGE:Trish said that

x+ 1

2 x− 2

−

3

x

=0 has two solutions. Do you agree?

Explain your answer.

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Copyright

©

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