To solve a rational equation, such as
+1 - =
, rewrite all the terms of the
equation as fractions with a common denominator. For example,
+1 - =
can be rewritten
as:

× +1× - × = ×

+ - =

Next, eliminate the denominator:

4*x*
^{2} - *x* + *x*
^{2} - *x* - 3 = *x*
^{2} + 5*x* - 6

Solve the equation:

5*x*
^{2} -2*x* - 3 = *x*
^{2} + 5*x* - 6

4*x*
^{2} - 7*x* + 3 = 0

(4*x* - 3)(*x* - 1) = 0

*x* = , 1

Since we cannot divide by zero, we must check to see if any of the
*x*
-values yield 0 in the denominator. If an
*x*
-value produces 0
in the denominator, it is not a solution.
*x* =
does
not produce 0 in any of the denominators, but
*x* = 1
does produce 0 in
one of the denominators. Thus,
*x* = 1
is not a solution. The solution
set is .

Remember to check all your solutions. If a number yields zero in any of the denominators, it is not a solution.