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, first 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 by a variable can introduce solutions that do not satisfy the original equation.

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What does it mean if a rational equation has no solution?

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If a rational equation has no solution, it means that there are no values for the variable that satisfy the equation, often due to division by zero.

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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.

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What is the result of multiplying both sides of a rational equation by the common denominator?

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Multiplying both sides by the common denominator eliminates the fractions, resulting in a polynomial equation that can be solved.

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What is the significance of the domain in rational equations?

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The domain of a rational equation is significant because it defines the values that the variable can take without causing division by zero.