Name Date
WORKSHEET 6.13: SOLVING FRACTIONAL EQUATIONS
-------------------------------------------------------------------------------------
Use the steps that follow to solve fractional equations:
- Multiply both sides of the equation by the least common denominator (LCD) to obtain
an equivalent equation that has no fractions. - Follow the steps for solving equations to find your solution.
- 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.
249
Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.