Partialbruchzerlegung/Q/1 durch (X^4+1)(X^2+1)/Aufgabe

a) Zeige, dass ${}X^{2}+1$ irreduzibel in ${}\mathbb {Q} [X]$ ist.

b) Zeige, dass ${}X^{4}+1$ irreduzibel in ${}\mathbb {Q} [X]$ ist. (Tipp: In ${}\mathbb {R} [X]$ gilt die Zerlegung ${}X^{4}+1={\left(X^{2}+{\sqrt {2}}X+1\right)}{\left(X^{2}-{\sqrt {2}}X+1\right)}$ )

c) Bestimme die Partialbruchzerlegung von

{\frac {1}{{\left(X^{2}+1\right)}{\left(X^{4}+1\right)}}}

in

{}\mathbb {Q} (X)

.

Zur Lösung, Alternative Lösung erstellen

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