Rational functions

This course is a part of Algebra II, a 23-course Topic series from Khan Academy.

Just as the polynomials are analogous to the integers, rational functions are analogous to the rational numbers. We will learn more about this analogy as we rewrite various rational expressions, and also think about their graphical behavior.

This course contains 9 segments:

Cancelling common factors

Learn how to simplify rational expressions by canceling factors that are shared by the numerator and the denominator. Sometimes this calls for factoring the numerator and the denominator in various ways.

End behavior of rational functions

Learn about the ways in which rational functions behave as x approaches positive or negative infinity. This gets interesting Learn how to determine this behavior for any kind of rational function.

Discontinuities of rational functions

Learn about the ways in which rational functions behave when their denominator is equal to zero. This gets interesting when vertical asymptotes are involved! Learn how to determine this behavior for any kind of rational function.

Graphs of rational functions

Combine your knowledge of intercepts, horizontal asymptotes, vertical asymptotes, and removable discontinuities, in order to analyze entire graphs of rational functions!

Modeling with rational functions

See some examples of how rational functions and equations can come in handy when solving real-world word problems.

Multiplying and dividing rational expressions

Learn how to multiply and divide rational expressions. You will be surprised to see how similar it is to multiplying and dividing fractions!

Adding and subtracting rational expressions intro

Learn how to add and subtract rational expressions. Like multiplication and division, this skill has a remarkable affinity to adding and subtracting fractions!

Adding and subtracting rational expressions (factored)

Adding and subtracting rational expressions (not factored)