Note:
If you would like an in-depth review of fractions, click on Fractions.
Solve for x in the following equation.
Example 3:
Rewrite the problem so that the denominator of every fraction is
factored.
Recall that you cannot divide by zero. Therefore, the first fraction is
valid if , 
or 
the second fraction is valid
if 
or 
and the third fraction is valid
is 
.If either 
5, or 
turn out to
be the solutions, you must discard them as extraneous solutions.
Multiply both sides by the least common multiple 
(the smallest number that all the
denominators will divide into evenly). This step will eliminate all the
denominators.
which is equivalent to
which can be rewritten as
which can be rewritten as
which can be simplified to
The answer is 
However, this may or may not be the
answer. You must check the solution with the original equation.
Check the solution 
by substituting 
in the original equation for x. If the left side of the equation equals the
right side of the equation after the substitution, you have found the
correct answer.
for x,
then is a solution.
You can also check your answer by graphing 
(formed by subtracting
the right side of the original equation from the left side). Look to see
where the graph crosses the x-axis; that will be the real solution. Note
that the graph crosses the x-axis at 
.
We have verified the solution two ways.
If you would like to work another example, click on Example
If you would like to test yourself by working some problems similar to this
example, click on Problem
If you would like to go back to the equation table of contents, click on
Contents
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S.O.S. Mathematics CyberBoard.
