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:

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:

Common Denominators

Now, let's apply this same strategy to the addition and subtraction of rational functions:

Rational Functions

Step 1) Find a common denominator by multiplying the denominators. So, (x + 3)(x - 2) becomes our common denominator in this case. Then, multiply each fraction by something equivalent to one, such as (x+3)/(x+3), to get each fraction in terms of that common denominator:

Rational Functions

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

Adding and Subtracting

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

Adding and Subtracting

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

Math Help

And that's our answer!

NOTE: To subtract rational functions, follow the same steps that you used to add 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 Mr. Feliz and Ted Wilcox
(c) 2005

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