Exercice
$\frac{8x^5+1}{2x^2-1}$
Solution étape par étape
1
Diviser $8x^5+1$ par $2x^2-1$
$\begin{array}{l}\phantom{\phantom{;}2x^{2}-1;}{\phantom{;}4x^{3}\phantom{-;x^n}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;}2x^{2}-1\overline{\smash{)}\phantom{;}8x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}-1;}\underline{-8x^{5}\phantom{-;x^n}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-8x^{5}+4x^{3};}\phantom{;}4x^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-1-;x^n;}\underline{-4x^{3}\phantom{-;x^n}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{3}+2x\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}+1\phantom{;}\phantom{;}\\\end{array}$
$4x^{3}+2x+\frac{2x+1}{2x^2-1}$
Réponse finale au problème
$4x^{3}+2x+\frac{2x+1}{2x^2-1}$