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

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Checking for extraneous solutions is important because multiplying both sides of an equation by a variable expression can introduce solutions that do not satisfy the original equation.

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What is the least common denominator (LCD)?

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The least common denominator (LCD) is the smallest expression that can be used as a common denominator for a set of fractions.

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7

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5

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3

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18

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3,-3, -3,3

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What is an extraneous solution?

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