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Solving Rational Equations

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.