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Unformatted text preview: 80 1 Solutions 35.
36.
37.
38.
39.
with 40. and . Thus, and with 41. with . But since, for any natural number ,
lower degree terms. Thus translating
the highest power of found in
will produce the same highest power
of in
. Since the same is also true for
, it follows that
. Thus, is a proper rational function.
42. If then where . Then and
. Hence
is a proper rational function.
43. Suppose
but not in
where
does not have a factor of
rule we have Thus . Then we can write
. By the quotient . Suppose
. Then the numerator
has a factor of . But this implies has a factor of . But this
is impossible since
. Hence
. ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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