So before we begin solving a rational equation, we examine it first to find the values that would make any denominators zero. But because the original equation may have a variable in a denominator, we must be careful that we don’t end up with a solution that would make a denominator equal to zero. Then, we will have an equation that does not contain rational expressions and thus is much easier for us to solve. We will multiply both sides of the equation by the LCD. We will use the same strategy to solve rational equations. We found the LCD of all the fractions in the equation and then multiplied both sides of the equation by the LCD to “clear” the fractions. We have already solved linear equations that contained fractions. Rational Expression Rational Equation 1 8 x + 1 2 y + 6 y 2 − 36 1 n − 3 + 1 n + 4 1 8 x + 1 2 = 1 4 y + 6 y 2 − 36 = y + 1 1 n − 3 + 1 n + 4 = 15 n 2 + n − 12 Rational Expression Rational Equation 1 8 x + 1 2 y + 6 y 2 − 36 1 n − 3 + 1 n + 4 1 8 x + 1 2 = 1 4 y + 6 y 2 − 36 = y + 1 1 n − 3 + 1 n + 4 = 15 n 2 + n − 12 Solve Rational Equations
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