Solve Rational Equations

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What is a rational equation?

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A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

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How do you solve a rational equation?

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To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting polynomial equation.

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x = -3.

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What is the importance of checking for extraneous solutions in rational equations?

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Checking for extraneous solutions is important because the process of solving can introduce solutions that do not satisfy the original equation.

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x = -\frac{5}{4}.

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What does it mean for a solution to be extraneous?

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An extraneous solution is a solution that emerges from the solving process but does not satisfy the original equation.

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x = 5.

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x = \frac{1}{6}.