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Definition and Domain of a Rational Expression - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

We have rational expressions whenever we have a fraction that has a polynomial in the numerator and/or in the denominator. An excluded value in the function is any value of the variable that would make the denominator equal to zero. To find the domain, list all the values of the variable that, when substituted, would result in a zero in the denominator.

A rational expression is a fraction where both our numerator and our denominator are polynomials so basically what that means is we have a fraction and the only powers of x's we have are whole positive numbers okay so we have a polynomial over a polynomial and more importantly our denominator cannot be equal to 0 we can't have a fraction where we're dividing by 0 so as long as our denominator is not equal to 0 we are fine.
Okay in addition we have our domain of a rational expression which is basically typically everything except for what makes this denominators 0 okay the only restrictions we're going to have then can divide by 0 so restrictions are when our denominator is equal to 0.

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