Note:
If you would like an in-depth review of fractions, click on Fractions.
Solve for x in the following equation.
Example 6:
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 if 
If either 1 or 
turn out to be the
solutions, you must discard them as extraneous solutions.
Multiply both sides by the least common multiple (x-1)(3x+1)
(the smallest expression that
all the denominators will divide into evenly).
which is equivalent to
which can be rewritten as
which can be rewritten as
which can be rewritten again as
The answer is 
Check this answer in 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 -4.333333. This means that the real solution is
-4.333333.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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