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 denominator are polynomials.

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How do you solve a rational equation?

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To solve a rational equation, you can find a common denominator, eliminate the fractions, and then solve the resulting polynomial equation.

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What is cross-multiplication?

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Cross-multiplication is a method used to solve equations involving two fractions by multiplying the numerator of one fraction by the denominator of the other.

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

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A rational equation has no solution if the equation leads to a contradiction, such as an impossible statement like 0 = 5.

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What is the first step in solving a rational equation?

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The first step is to identify any restrictions on the variable that would make the denominator zero.

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What is a common denominator?

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A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be combined or compared.

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What is the importance of checking your solution in rational equations?

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Checking your solution is important to ensure that it does not make any denominator zero, which would invalidate the solution.

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What is an extraneous solution?

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

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How do you find the least common denominator (LCD)?

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To find the least common denominator, identify the prime factors of each denominator and take the highest power of each factor.

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What is the process of simplifying a rational expression?

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Simplifying a rational expression involves factoring the numerator and denominator and then canceling any common factors.