Solving Equations with Rational Expressions

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In this section, we review how to solve an equation with rational expressions. First and foremost, our goal is to clear the denominators. In order to do this, we multiply both sides of the equation by the LCD (least common denominator) of all denominators. Once the denominators are cleared, we can easily solve our equation. We report our proposed solutions, but we must check each in the original equation. The reason for this is simple: we can never divide by zero. If we substitute a value in for our variable in the original equation, and it results in a zero denominator, we must reject that solution. For this reason, we must always check each solution to guard against errors. Alternatively, we can find the restricted values before we begin the problem. We can then compare our proposed solutions to the restricted values and reject any solution that matches a restricted value.
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