Note:
If you would like an in-depth review of fractions, click on Fractions.
Solve for x in the following equation.
Example 4:
Recall that you cannot divide by zero. Therefore, the first fraction is
valid if , 
and the second fraction is valid if 
If either 
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. 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 x=10. However, this may or may not be the answer. You must
check the solution with the original equation.
Check the solution x=10 by substituting 10 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 10.
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
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