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Questions and Answers
What is a rational expression?
What is a rational expression?
What does the difference of squares refer to?
What does the difference of squares refer to?
two perfect square terms being subtracted
What is a perfect square trinomial?
What is a perfect square trinomial?
an expression consisting of three terms where the first and last terms are perfect squares, and the middle term is twice the product of the square roots of those terms
The steps to simplifying rational expressions include factoring the numerator and denominator, identifying the restrictions, and ___
The steps to simplifying rational expressions include factoring the numerator and denominator, identifying the restrictions, and ___
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What is a discontinuity?
What is a discontinuity?
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What is an asymptote?
What is an asymptote?
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What are vertical asymptotes?
What are vertical asymptotes?
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What are oblique asymptotes?
What are oblique asymptotes?
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What is an extraneous solution?
What is an extraneous solution?
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What is a non-extraneous solution?
What is a non-extraneous solution?
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Study Notes
Rational Expressions
- Defined as a fraction containing a polynomial in both the numerator and the denominator.
Difference of Squares
- Formed by subtracting two perfect square terms.
Perfect Square Trinomial
- Consists of three terms.
- The first and last terms are perfect squares.
- The middle term equals twice the product of the square roots of the first and last terms.
Steps to Simplifying Rational Expressions
- Factor both the numerator and denominator when possible.
- Identify any restrictions on the variables.
- Simplify the expression by canceling common factors.
Discontinuity
- Refers to points in a rational function's graph where it does not exist.
Asymptote
- An imaginary line that approaches the graph of a rational function but never touches it.
Vertical Asymptotes
- These imaginary lines extend infinitely upwards and downwards along the coordinate plane.
Oblique Asymptotes
- Lines that are neither vertical nor horizontal.
- They extend diagonally along the graph of a function.
Extraneous Solution
- A solution derived from a radical equation that does not satisfy the original equation.
Non-extraneous Solution
- A solution that satisfies the original equation, confirming its validity.
Studying That Suits You
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Description
Test your knowledge with these flashcards from Algebra 2 Module 5. This quiz covers key concepts such as rational expressions, difference of squares, and perfect square trinomials. Perfect for reviewing essential algebraic expressions and their definitions.
