Unit 4 Review CP - Rational Expressions & Equations

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Define Rational Expression.

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A rational expression is a fraction where the numerator and the denominator are both polynomials.

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What is the process to simplify a rational expression?

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To simplify a rational expression, factor both the numerator and the denominator, then cancel any common factors.

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

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To find the LCD, factor each denominator and take the highest power of each factor that appears.

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What is the first step in solving a rational equation?

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The first step is to find a common denominator for all terms in the equation.

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What is the result of multiplying two rational expressions?

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The result is obtained by multiplying the numerators together and the denominators together, then simplifying.

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What is the significance of checking for extraneous solutions?

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Checking for extraneous solutions ensures that the solutions found are valid in the context of the original equation.