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Section Rational Functions
[provisional cross-reference: WORK-IN-PROGRESS]Rational functions are a fundamental concept in algebra and calculus, and they play a significant role in differential equations. A rational function is defined as the ratio of two polynomials.
π Definition 318 . Rational Function.
A
rational function is a function that is the division of two polynomials.
For example, the following are rational functions in the variables \(s\text{,}\) \(x\text{,}\) and \(t\text{,}\) respectively:
\begin{equation*}
\frac{s^2 + 3s + 2}{s - 1}, \quad \frac{2x^3 - 5x + 7}{x^2 - 4}, \quad \frac{1}{t^2 + 1}\text{.}
\end{equation*}
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