Übung
$\frac{\left(4c^4+5c^3-9c^2-5c+20\right)}{\left(c^2-2\right)}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $4c^4+5c^3-9c^2-5c+20$ durch $c^2-2$
$\begin{array}{l}\phantom{\phantom{;}c^{2}-2;}{\phantom{;}4c^{2}+5c\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}c^{2}-2\overline{\smash{)}\phantom{;}4c^{4}+5c^{3}-9c^{2}-5c\phantom{;}+20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}c^{2}-2;}\underline{-4c^{4}\phantom{-;x^n}+8c^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4c^{4}+8c^{2};}\phantom{;}5c^{3}-c^{2}-5c\phantom{;}+20\phantom{;}\phantom{;}\\\phantom{\phantom{;}c^{2}-2-;x^n;}\underline{-5c^{3}\phantom{-;x^n}+10c\phantom{;}\phantom{-;x^n}}\\\phantom{;-5c^{3}+10c\phantom{;}-;x^n;}-c^{2}+5c\phantom{;}+20\phantom{;}\phantom{;}\\\phantom{\phantom{;}c^{2}-2-;x^n-;x^n;}\underline{\phantom{;}c^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}c^{2}-2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}5c\phantom{;}+18\phantom{;}\phantom{;}\\\end{array}$
$4c^{2}+5c-1+\frac{5c+18}{c^2-2}$
Endgültige Antwort auf das Problem
$4c^{2}+5c-1+\frac{5c+18}{c^2-2}$