Note:
If you would like an in-depth review of fractions, click on Fractions
Solve for x in the following equation.
Example 5:
Recall that you cannot divide by zero. Therefore, the first fraction is
valid if , and the second fraction is valid if If either -1 or -2 turn out to be the solutions, you must
discard them as extraneous solutions.
Multiply both sides by the least common multiple (x+1)(x+2)
(the smallest expression that
all the denominators will divide into evenly).
which is equivalent to
which can be rewritten as
which can be rewritten as
which can be rewritten again as
The answers are 1 and -3.
Check this answers in the original equation.
Check the solution x=1 by substituting 1 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 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.
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 1 and -3. This means that the real solutions are 1 and -3.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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