Why division by zero is the ultimate rule of rational expressions
In short: Understanding how to match rational functions to their graphs requires mastering the behavior of polynomials in fractions. This video explores the foundational rules of these expressions, from simplifying terms to identifying critical restrictions.
A rational expression is defined as a fraction where both the numerator and denominator are polynomials. A fundamental rule in algebra is that division by zero is undefined; therefore, when working with rational expressions, one must always identify values that would cause the denominator to equal zero.
The video covers techniques for reducing these expressions to lowest terms by canceling common factors. It highlights a frequent pitfall: students often incorrectly cancel terms separated by addition or subtraction signs. To properly cancel a factor, it must multiply the entire numerator and denominator.
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Sources
- Summary by Intellect · source: Matching rational functions to their graphs | Rational expressions | Algebra II | Khan Academy
- Also: Algebra - Rational Expressions
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