Questions and Answers
What is a rational expression?
What does it mean for an expression to be simplified?
To write an answer in as few terms and factors as possible.
Define an equivalent expression.
Algebraic expressions that are equivalent to each other for any values of their variables.
What is a factor?
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What is the least common multiple?
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What does least common denominator refer to?
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What is long division?
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What is standard form?
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Define a complex rational expression.
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What is a rational equation?
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What does clearing the denominators involve?
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What is an extraneous solution?
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What is an asymptote?
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Study Notes
Rational Expressions & Equations Vocabulary
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Rational Expression: Represents the quotient of two polynomials, forming a fraction with a polynomial numerator and polynomial denominator.
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Simplified: Refers to an expression expressed with the minimum number of terms and factors, enhancing clarity.
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Equivalent Expression: Describes algebraic expressions that yield the same value for all variable inputs, critical for manipulation in equations.
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Factor: The components that, when multiplied together, result in a product; understanding factors is essential for simplifying expressions.
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Least Common Multiple (LCM): The smallest multiple shared by two or more numbers, important for finding common denominators in fractions.
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Least Common Denominator (LCD): The smallest integer which serves as a common denominator for two or more fractions, facilitating addition or subtraction of fractions.
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Long Division: A method used to simplify complex division problems into manageable steps, combining division, multiplication, and subtraction.
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Standard Form: A representation of numbers in a conventional way, especially large or small numbers, making calculations more straightforward.
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Complex Rational Expression: A fraction where either the numerator, denominator, or both are rational expressions, increasing complexity in mathematical operations.
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Rational Equation: An equation featuring at least one rational expression, typically needing specific techniques to solve.
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Clearing the Denominators: The process of eliminating variables from denominators by multiplying both sides of the equation by the least common denominator.
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Extraneous Solution: Solutions derived during the equation-solving process that do not satisfy the original equation, often requiring verification.
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Asymptote: Refers to a line that a graph approaches but never intersects, indicating behavior of functions at extreme values.
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Test your understanding of key terms related to rational expressions and equations with this vocabulary flashcard quiz. Each term is defined clearly to help you grasp the concepts better. Perfect for reinforcing your knowledge in algebra.