Note:
If you would like an in-depth review of fractions, click on Fractions.
Solve for x in the following equation.
Example 2:
Recall that you cannot divide by zero. Therefore, the first fraction is
valid if , 
the second fraction is valid if 
and the third fraction is valid is 
.If
either 
or 
turn out to be the solutions, you
must discard them as extraneous solutions.
Rewrite the problem so that every denominator is factored
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
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