Note:
For an in-depth review on fractions, click on Fractions.
Solve for x in the following equation.
Problem 5.1a:
Answer:No Solution
Solution:
Recall that you cannot divide by zero. Therefore, the first fraction is
valid if , 
or 
,the second fraction is
valid if 
and the third fraction is valid is 
. If either 0 or 3 turn out to be solutions, you must
discard them as extraneous solutions.
The least least common multiple x(x-3) (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
Since our initial constraint was that , there is no solution.
If you forgot to make this observation, you would have caught the mistake in
the check.
Check the solution x=3 by substituting 3 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.
The fraction 
is undefined
because you cannot divide by zero. You might say ''well what about the
fraction 
If you are adding 100 fractions and 99 are good and
one is undefined, the entire expression is undefined.
is also undefined.
Undefined means there is no solution.
(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 never crosses the x-axis. This means that there are no real
solutions.
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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