Rational Functions
A rational function is basically a division of two polynomial functions. That is, it is a polynomial divided by another polynomial.
Domain of a Rational Function: The domain of a rational expression is the set of all values for the variable that make the expression defined.
Simplifying (or reducing) a Rational Expression
Step 1: Factor the numerator and the denominator completely.
Step 2: Mention all the excluded values, find the domain of definition.
Step 3: Apply the fundamental principle of rational expressions to divide out all common factors that the numerator and the denominator have.
Sometimes, the process of factorizing will be very important in simplifying fractions. Here are some examples of possible simplifications, and some warnings of what can’t be done.
If you have always found this sort of thing difficult, it may help you here to highlight the matching parts which are cancelling with each other in the same color.
Read the explanation below to learn more about rational functions.
Practice: Define and simplify rational expressions to answer the exercise below.