Rational Expressions Vocabulary

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Questions and Answers

What is a rational expression?

  • An expression that is always equal to zero
  • An expression involving irrational numbers
  • An expression that can be written as a quotient of two polynomials (correct)
  • An expression involving only integers

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?

<p>The numbers multiplied together that give a product.</p> Signup and view all the answers

What is the least common multiple?

<p>The lowest number that is a common multiple of two or more numbers.</p> Signup and view all the answers

What does least common denominator refer to?

<p>The smallest integer that allows two or more fractions to have the same denominator.</p> Signup and view all the answers

What is long division?

<p>Breaks a large division problem into repeated steps of division, multiplication, and subtraction.</p> Signup and view all the answers

What is standard form?

<p>A way of writing very large or very small numbers easily.</p> Signup and view all the answers

Define a complex rational expression.

<p>An algebraic expression written as a fraction where the numerator and/or denominator contains a rational expression.</p> Signup and view all the answers

What is a rational equation?

<p>An equation with at least one rational expression.</p> Signup and view all the answers

What does clearing the denominators involve?

<p>Multiplying both sides of a rational equation by the least common denominator.</p> Signup and view all the answers

What is an extraneous solution?

<p>Solutions acquired during the solving of an equation that do not hold true.</p> Signup and view all the answers

What is an asymptote?

<p>A line that a graph approaches but never reaches.</p> Signup and view all the answers

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Study Notes

Rational Expressions & Equations Vocabulary

  • Rational Expression: Represents the quotient of two polynomials, forming a fraction with a polynomial numerator and polynomial denominator.

  • Simplified: Refers to an expression expressed with the minimum number of terms and factors, enhancing clarity.

  • Equivalent Expression: Describes algebraic expressions that yield the same value for all variable inputs, critical for manipulation in equations.

  • Factor: The components that, when multiplied together, result in a product; understanding factors is essential for simplifying expressions.

  • Least Common Multiple (LCM): The smallest multiple shared by two or more numbers, important for finding common denominators in fractions.

  • Least Common Denominator (LCD): The smallest integer which serves as a common denominator for two or more fractions, facilitating addition or subtraction of fractions.

  • Long Division: A method used to simplify complex division problems into manageable steps, combining division, multiplication, and subtraction.

  • Standard Form: A representation of numbers in a conventional way, especially large or small numbers, making calculations more straightforward.

  • Complex Rational Expression: A fraction where either the numerator, denominator, or both are rational expressions, increasing complexity in mathematical operations.

  • Rational Equation: An equation featuring at least one rational expression, typically needing specific techniques to solve.

  • Clearing the Denominators: The process of eliminating variables from denominators by multiplying both sides of the equation by the least common denominator.

  • Extraneous Solution: Solutions derived during the equation-solving process that do not satisfy the original equation, often requiring verification.

  • Asymptote: Refers to a line that a graph approaches but never intersects, indicating behavior of functions at extreme values.

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