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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What does it mean to solve a rational equation by cross-multiplying?

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Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction to eliminate the fractions and create a linear equation.

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x = 5.5

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k = 3 or k = -3.

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How do you check if your solution to a rational equation is valid?

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Substitute the solution back into the original equation to ensure both sides are equal and check that no denominators are zero.

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What is the importance of finding a common denominator in rational equations?

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Finding a common denominator allows you to combine fractions and simplify the equation, making it easier to solve.

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x = 5.5.

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

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It means that there are no values for the variable that will satisfy the equation, often due to a contradiction.

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x = 0.