EQUATIONS INVOLVING FRACTIONS (RATIONAL EQUATIONS)


Note:




If you would like an in-depth review of fractions, click on Fractions



Solve for x in the following equation.


Example 5:tex2html_wrap_inline155tex2html_wrap_inline172


Recall that you cannot divide by zero. Therefore, the first fraction is valid if , tex2html_wrap_inline174 and the second fraction is valid if tex2html_wrap_inline176 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).


eqnarray37


eqnarray44



which is equivalent to


eqnarray52



which can be rewritten as


eqnarray66



which can be rewritten as


eqnarray74



which can be rewritten again as


eqnarray87


eqnarray91


eqnarray95


eqnarray99


eqnarray103



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.


Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 1 for x, then x=1 is a solution.


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 equal to the right side of the original equation after we substitute the value -3 for x, then x=-3 is a solution.


You can also check your answer by graphing tex2html_wrap_inline200 (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.








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Author: Nancy Marcus

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