If you would like an in-depth review of fractions, click on Fractions.
Solve for x in the following equation.
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 turn out to be the solutions, you must discard them as extraneous solutions.
The first step is always to rewrite the problem so that every denominator is factored. In this problem, the denominator does not need factoring.
Multiply both sides of the equation by the least common multiple (the smallest number that all the denominators will divide into evenly). This step will eliminate all the denominators in the equation. The resulting equation may be equivalent (same solutions as the original equation) or it may not be equivalent (extraneous solutions),
which is equivalent to
which can be rewritten as
which can be rewritten again as
Solve for x using the quadratic formula:
The exact answers are and the approximate answers are x=0.758872343938 and x=-0.658872343938.
Check the answer in the original equation.
Check the solution by substituting x=0.758872343938 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.
Check the solution by substituting x=-0.658872343938 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 equals the right side of the original equation after we substitute the value -0.658872343938 for x, we have verified that 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; the intercept(s) will be the real solution(s). Note that the graph crosses the x-axis in two places: -0.658872343938 and 0.758872343938.
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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