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Rational Functions

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A series of free, online Basic Algebra Lessons.

In this lesson, we will learn

  • about rational functions
  • how to simplify rational functions with factoring

Introduction to Rational Functions

We have rational functions 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.

An introduction to rational functions, the reciprocal function, and vertical and horizontal asymptotes.

A couple of examples on graphing rational functions.

Simplifying Rational Functions with Factoring and GCFs

Simplifying rational expressions combines everything learned about factoring common factors and polynomials. When simplifying rational functions, factor the numerator and denominator into terms multiplying each other and look for equivalents of one (something divided by itself). Include parenthesis around any expression with a "+" or "-" and if all terms cancel in the numerator, there is still a one there.

This video looks at simplifying rational expressions using factoring is key. There are four examples in this video. Simplifying Rational Expressions using factoring Simplifying Rational Expressions Simplifying Rational Expression

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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