The Method of Partial Fractions

4. The denominator has a repeated linear factor; so we use the setup

displaymath580

Note that the least common denominator for this problem is . Here is the final answer:

displaymath581

Some fine points.

(1) All examples so far have dealt with fractions, where the degree of the numerator is less than the degree of the denominator. For good reason: If the degree on top is at least as big as the degree on the bottom, one can first perform polynomial division, and then apply the method of partial fractions to the remainder term:

displaymath621

and then use tex2html_wrap_inline625 to obtain

Try it yourself!

Helmut Knaust
Fri Jul 5 13:54:22 MDT 1996