Adding and Subtracting Rational Functions
(view a printable version of this lesson)
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 Mr. Feliz and Ted Wilcox
(c) 2005
