Exercise
https://texercises.com/exercise/partialbruchzerlegung-bei-mehrfachen-ganzzahligen-nullstellen/
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Exercise:
Die Nenner der folgen Brüche lassen sich vollständig in Linearfaktoren mit ganzzahligen allenfalls mehrfachen Nullstellen zerlegen. Stelle jeden Bruch als Summe von Partialbrüchen dar. nprvmulticols abcliste %a abc displaystyle fracx^-x+x^-x^+x- %b abc displaystyle fracx^+x+x^+x^- %c abc displaystyle fracx^-x+x^-x^+ %d abc displaystyle frac-x^+x+x^+x^+x+ %e abc displaystyle fracx^-x+x^-x^+ %f abc displaystyle -fracx^+x+x^+x^+x+ %g abc displaystyle fracx^+x^-x^+x- %h abc displaystyle fracx^+x+x^+x^+x+ %i abc displaystyle fracx^-x+x^-x^+x- abcliste nprvmulticols

Solution:
%maxima %i expr : /x+ + /x- - /x-; %i ratsimpexpr; abcliste %a abc fracx^-x+x^-x^+x- fracxmathop-mathop+fracleft xmathop-right ^mathop+fracxmathop- %b abc fracx^+x+x^+x^- fracxmathop+mathop+fracleft xmathop+right ^mathop+fracxmathop- %c abc fracx^-x+x^-x^+ fracxmathop+mathop+fracxmathop-mathop+fracleft xmathop-right ^ %d abc frac-x^+x+x^+x^+x+ mathop-left fracxmathop+right mathop+fracxmathop+mathop+fracleft xmathop+right ^ %e abc fracx^-x+x^-x^+ fracxmathop+mathop+fracxmathop-mathop+fracleft xmathop-right ^ %f abc -fracx^+x+x^+x^+x+ fracxmathop+mathop+fracleft xmathop+right ^mathop-fracxmathop+ %g abc fracx^+x^-x^+x- fracxmathop-mathop+fracleft xmathop-right ^mathop+fracleft xmathop-right ^ %h abc fracx^+x+x^+x^+x+ fracxmathop+mathop+fracleft xmathop+right ^mathop+fracleft xmathop+right ^ %i abc fracx^-x+x^-x^+x- fracxmathop-mathop+fracleft xmathop-right ^mathop+fracleft xmathop-right ^ abcliste
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Exercise:
Die Nenner der folgen Brüche lassen sich vollständig in Linearfaktoren mit ganzzahligen allenfalls mehrfachen Nullstellen zerlegen. Stelle jeden Bruch als Summe von Partialbrüchen dar. nprvmulticols abcliste %a abc displaystyle fracx^-x+x^-x^+x- %b abc displaystyle fracx^+x+x^+x^- %c abc displaystyle fracx^-x+x^-x^+ %d abc displaystyle frac-x^+x+x^+x^+x+ %e abc displaystyle fracx^-x+x^-x^+ %f abc displaystyle -fracx^+x+x^+x^+x+ %g abc displaystyle fracx^+x^-x^+x- %h abc displaystyle fracx^+x+x^+x^+x+ %i abc displaystyle fracx^-x+x^-x^+x- abcliste nprvmulticols

Solution:
%maxima %i expr : /x+ + /x- - /x-; %i ratsimpexpr; abcliste %a abc fracx^-x+x^-x^+x- fracxmathop-mathop+fracleft xmathop-right ^mathop+fracxmathop- %b abc fracx^+x+x^+x^- fracxmathop+mathop+fracleft xmathop+right ^mathop+fracxmathop- %c abc fracx^-x+x^-x^+ fracxmathop+mathop+fracxmathop-mathop+fracleft xmathop-right ^ %d abc frac-x^+x+x^+x^+x+ mathop-left fracxmathop+right mathop+fracxmathop+mathop+fracleft xmathop+right ^ %e abc fracx^-x+x^-x^+ fracxmathop+mathop+fracxmathop-mathop+fracleft xmathop-right ^ %f abc -fracx^+x+x^+x^+x+ fracxmathop+mathop+fracleft xmathop+right ^mathop-fracxmathop+ %g abc fracx^+x^-x^+x- fracxmathop-mathop+fracleft xmathop-right ^mathop+fracleft xmathop-right ^ %h abc fracx^+x+x^+x^+x+ fracxmathop+mathop+fracleft xmathop+right ^mathop+fracleft xmathop+right ^ %i abc fracx^-x+x^-x^+x- fracxmathop-mathop+fracleft xmathop-right ^mathop+fracleft xmathop-right ^ abcliste
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Tags
mathematik, partialbruchzerlegung
Content image
Difficulty
(3, default)
Points
9 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration