If you would like an in-depth review of fractions, click on Fractions.
Solve for x in the following equation.
Problem 5.4 a:
Rewrite the equation such that all the denominators are 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 is . If 1, 6 or -5 turn out to be the solutions, you must discard them as extraneous solutions.
Multiply both sides of the equation by an expression that represents the lowest common denominator. The expression is the smallest expression because it is the smallest expression that is divisible by all three denominators.
This equation can be written as
Multiply the fractions where indicated.
Rearrange the factors in the numerators and rewrite the equations as
Rewrite the equation once again as
Simplify the last equation and solve for x.
There are two real solutions: x=3,x=5
Check the two answers in the original equation.
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.
Since the left side of the original equation is not equal to the right side of the original equation after we substitute the value 3 for x, then x=3is a solution.
Check the solution x=5 by substituting 5 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 not equal to the right side of the original equation after we substitute the value 5 for x, then x=5is a solution.
You can also check your answer by graphing
This means that there are two real solutions and the solutions are x=3,5.
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