Here is a cool, easy-to-use, method of doing partial fractions by using a little

complex analysis. Don't be put off by the words 'complex and analysis'. It's

easy and a nice alternative to the standard method of using A and B and

what not.

Let's use the example

When we factor the denominator as we would by the standard method, we get

Now, f(x) has simple poles at x=4 and x=2. See?. Those are the values that result in division by 0.

Now, we take the limits as such:

The other:

There, we have the numerators in our partial fraction decomposition.

And we get:

Now, f(x)-r(x) has no poles in the complex plane, but the function is bounded so we must have a constant.

Since

we have:

I hope you find this helpful and a nice/fun alternative to doing PFD's.