Note:
For an in-depth review on fractions, click on Fractions.
Solve for x in the following equation.
Problem 5.1d: 
Answer: 
Solution:
Rewrite the problem so that every denominator is fully factored.
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 
or 
If either 8 or -1 turn out to be solutions, you must
discard them as extraneous solutions.
The least least common multiple (the smallest expression that all the
denominators will divide into evenly) is 
. Multiply both sides of the equation by the least common
multiple
which is equivalent to
which can be rewritten as
which can be rewritten as
which can be rewritten as
The answers are 
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.
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.
Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value 
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 
. This means that the real solutions
are 
.
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