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 tex2html_wrap_inline619. 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

displaymath622


Try it yourself!

tex2html_wrap_inline639


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

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