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

Teaching Notes 6.13: Solving Fractional Equations

Solving fractional equations involves not only finding the least common denominator (LCD) but

also checking if the solution satisfies the original equation. A common mistake occurs when

students find a solution to a fractional equation that makes the denominator of the original

equation equal to zero and they include that solution as a solution to the equation.

1. Explain that a fractional equation is an equation that has a variable in the denominator of
   one or more terms.


2. Explain that solving a fractional equation involves the same steps as solving equations with
   fractional coefficients. Students must find the least common denominator and multiply both
   sides of the equation by the LCD to obtain an equivalent equation that has no fractions. Once
   the equation is solved, students must check their solution by considering if there are any
   restrictions on the variable in the original equation.


3. Offer this example:
   3 y− 6
   y− 2
   − 3 =0. Demonstrate that multiplying both sides by the least
   common denominator (y−2) results in the equation 3y− 6 − 3 y+ 6 =0, which is true for
   all real numbers. Because the denominator of the original equation cannot equal 0,y=2.
   The solution must be modified so that the solution to the original fractional equation is all
   real numbers except 2.


4. Review the information and example on the worksheet with your students. Make sure that
   your students understand the steps for solving equations. If students find a solution, they
   must be sure that it will not make the denominator of any term in the original equation equal
   to zero. Note that when they obtain a false statement, there is no solution.

EXTRA HELP:

Multiply every term of the equation by the LCD.

ANSWER KEY:

(1)n= 2 (2)x= 6 (3)No solution (4)All real numbers except 2. (5)x= 9

------------------------------------------------------------------------------------------

(Challenge)Trish is correct. The solutions arex=3andx=2. The answers were obtained by

solving the fractional equation.

------------------------------------------------------------------------------------------

248 THE ALGEBRA TEACHER’S GUIDE