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.
Undefined means there is no solution.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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