Rational expressions are algebraic fractions with polynomial numerators and denominators. They are essential in fields like engineering and mathematics, particularly in control systems. Simplifying these expressions involves factoring and reducing them to their simplest form by canceling common factors. Proper rational expressions have a lower degree numerator, while improper ones have a numerator degree that is equal to or higher than the denominator's.
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Rational expressions are algebraic fractions with polynomials in both the numerator and denominator
Rational expressions are commonly used in engineering to represent transfer functions in control systems
Rational expressions can be identified by checking if both the numerator and denominator are polynomials
Proper rational expressions have a numerator with a lower degree than the denominator
Improper rational expressions have a numerator with a degree equal to or greater than the denominator
The degree of a polynomial is the highest exponent of the variable in its terms
Simplifying rational expressions involves reducing them to their most basic form by eliminating common factors from the numerator and denominator
Factoring is a powerful tool for simplifying rational expressions by exposing common factors that can be canceled
Equivalent rational expressions represent the same value and can be identified by manipulating the expressions to show their equivalence
Rational expressions can be categorized as proper or improper based on the degrees of their polynomials
Simplifying rational expressions involves canceling out common factors after factoring the polynomials
Mastery of rational expressions is achieved through practice and enables students to effectively handle them in various mathematical situations
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In ______, rational expressions often represent ______ functions in control systems.
engineering
transfer
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Definition of proper rational expression
Numerator degree less than denominator degree.
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Example of improper rational expression
Numerator degree equal to or greater than denominator degree.
