Exercice
$\frac{\left(48x^4+18x^2-1\right)}{x^2+x-1}$
Solution étape par étape
1
Diviser $48x^4+18x^2-1$ par $x^2+x-1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}-1;}{\phantom{;}48x^{2}-48x\phantom{;}+114\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}-1\overline{\smash{)}\phantom{;}48x^{4}\phantom{-;x^n}+18x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-1;}\underline{-48x^{4}-48x^{3}+48x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-48x^{4}-48x^{3}+48x^{2};}-48x^{3}+66x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-1-;x^n;}\underline{\phantom{;}48x^{3}+48x^{2}-48x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}48x^{3}+48x^{2}-48x\phantom{;}-;x^n;}\phantom{;}114x^{2}-48x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-1-;x^n-;x^n;}\underline{-114x^{2}-114x\phantom{;}+114\phantom{;}\phantom{;}}\\\phantom{;;-114x^{2}-114x\phantom{;}+114\phantom{;}\phantom{;}-;x^n-;x^n;}-162x\phantom{;}+113\phantom{;}\phantom{;}\\\end{array}$
$48x^{2}-48x+114+\frac{-162x+113}{x^2+x-1}$
Réponse finale au problème
$48x^{2}-48x+114+\frac{-162x+113}{x^2+x-1}$