Questions and Answers
What is a rational expression?
An algebraic expression whose numerator and denominator are polynomials and whose denominator has a degree greater than or equal to 1.
What is a simplified rational expression?
A polynomial expression whose numerator and denominator have no factors in common.
What is the domain of a rational expression?
All real numbers except those that make the denominator equal to zero.
What is a complex fraction?
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What is a rational equation?
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What is a radical (or square-root) equation?
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What is the index in a radical?
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What is a rational exponent?
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What is an extraneous solution?
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Study Notes
Rational Expressions and Equations
- A rational expression is a ratio of algebraic expressions where both the numerator and denominator are polynomials; the denominator must have a degree of at least one.
- A simplified rational expression occurs when the numerator and denominator share no common factors; this ensures the expression is in its simplest form.
- The domain of a rational expression includes all real numbers except those that make the denominator zero, as division by zero is undefined.
Types of Fractions and Equations
- A complex fraction is defined as a fraction that includes one or more fractions within either the numerator, the denominator, or both, complicating the fraction's evaluation.
- A rational equation entails an equation featuring one or more rational expressions, often requiring solving techniques to eliminate the fractions.
- A radical (or square-root) equation is characterized by containing a variable inside a radical or square root, affecting how solutions are approached.
Elements of Radicals
- The index in the context of a radical indicates the root being taken, denoted as 'n' before the radical sign; for square roots, this is inherently 2 when not specified.
- A rational exponent refers to an exponent expressed as a fraction m/n, allowing for conversion of expressions such that b^(m/n) represents the nth root of b raised to the m-th power.
Solutions in Algebra
- An extraneous solution emerges during problem-solving but does not satisfy the original equation, highlighting the importance of verifying solutions to ensure validity.
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Explore key concepts related to rational and radical equations in Algebra 2 through this quiz. Familiarize yourself with critical terms and their definitions to strengthen your understanding of these essential mathematical topics.