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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Define the term 'LCD' in the context of rational equations.

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LCD stands for Least Common Denominator, which is the smallest expression that can be used as a common denominator for two or more fractions.

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To find the LCD, factor the denominators and take the highest power of each factor that appears in any of the denominators.

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What is the first step in solving a rational equation?

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The first step is to identify the LCD of all the fractions in the equation.

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What happens when you multiply both sides of a rational equation by the LCD?

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Multiplying both sides by the LCD eliminates the fractions, allowing you to solve the resulting polynomial equation.

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x = -2, 8

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x = 0

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Front

What is the significance of identifying restrictions in rational equations?

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Identifying restrictions is crucial because it helps to determine values that would make the denominator zero, which are not allowed in rational expressions.