Adding and Subtracting Rational Functions

First of all, a rational function is pretty much just the division of two polynomial functions. For example, the following is a rational function:

When adding or subtracting rational functions, you must find a common denominator as you might do with regular fractions.

For example, to add 1/2 and 1/3, you might do the following:

Now let's apply this same strategy to the adding and subtracting of rational functions:

1) Find a common denominator by multiplying the denominators. So, (x + 3)(x - 2) becomes our common denominator in this case. Multiply each fraction by 1 to get each fraction in terms of that common denominator:

Here's what we have so far. Just multiply out the top and we will be ready to add the two fractions:

Now add the numerators just like you would with two simple fractions:

Finally we want to expand the denominator as well to give us the resulting rational function:

And that's our answer!

NOTE: To subtract rational functions, follow the same steps for addition of rational functions, but just subtract the numerators instead of adding them.

For information on rational functions, try a search on Google or this lesson on rational functions.

By Guido Feliz, Jr and Ted Wilcox
(c) 2005