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Extraneous Solution to a Rational Equation
An extraneous solution to a rational equation is a value that emerges from the algebraic solving process but would cause one or more of the expressions in the original equation to be undefined. Because rational expressions have denominators that must not equal zero, any algebraic solution that produces a zero denominator in the original equation is invalid and must be discarded. Although such a value satisfies the manipulated form of the equation, it does not satisfy the original equation itself. This is why it is essential to check every solution of a rational equation against the denominators of the original expressions before accepting it as valid.
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