AA C&C Unit 7 FLASHCARD 2: Add/Sub & Solve Rational Equations

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What is a rational expression?

Back

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

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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 into its prime factors and take the highest power of each factor.

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What is the process for adding rational expressions?

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1. Find the least common denominator (LCD). 2. Rewrite each expression with the LCD. 3. Add the numerators and simplify.

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What is the difference between a proper and improper rational expression?

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A proper rational expression has a degree in the numerator less than the degree in the denominator, while an improper rational expression has a degree in the numerator greater than or equal to the degree in the denominator.

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What does it mean to simplify a rational expression?

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Simplifying a rational expression means reducing it to its lowest terms by canceling common factors in the numerator and denominator.

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How do you solve a rational equation?

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1. Find a common denominator. 2. Multiply both sides by the common denominator to eliminate fractions. 3. Solve the resulting equation.

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What is the importance of checking for extraneous solutions in rational equations?

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Extraneous solutions are solutions that do not satisfy the original equation. Checking ensures that the solutions are valid.

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What is the formula for finding the common denominator of two rational expressions?

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The common denominator is the product of the unique factors from both denominators, raised to the highest power that appears in either denominator.

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What is the process for dividing rational expressions?

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What is factoring in the context of rational expressions?

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Factoring involves rewriting a polynomial as a product of its factors, which can help simplify rational expressions.