Übung
$\frac{x^4-13x^3+2x^2-5x+9}{x^2-1}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $x^4-13x^3+2x^2-5x+9$ durch $x^2-1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-1;}{\phantom{;}x^{2}-13x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-1\overline{\smash{)}\phantom{;}x^{4}-13x^{3}+2x^{2}-5x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-1;}\underline{-x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+x^{2};}-13x^{3}+3x^{2}-5x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-1-;x^n;}\underline{\phantom{;}13x^{3}\phantom{-;x^n}-13x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}13x^{3}-13x\phantom{;}-;x^n;}\phantom{;}3x^{2}-18x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-1-;x^n-;x^n;}\underline{-3x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{;;-3x^{2}+3\phantom{;}\phantom{;}-;x^n-;x^n;}-18x\phantom{;}+12\phantom{;}\phantom{;}\\\end{array}$
$x^{2}-13x+3+\frac{-18x+12}{x^2-1}$
Endgültige Antwort auf das Problem
$x^{2}-13x+3+\frac{-18x+12}{x^2-1}$