Esercizio
$\frac{x^5-1}{2x^2-5}$
Soluzione passo-passo
1
Dividere $x^5-1$ per $2x^2-5$
$\begin{array}{l}\phantom{\phantom{;}2x^{2}-5;}{\frac{1}{2}x^{3}\phantom{-;x^n}+\frac{\frac{5}{2}}{2}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}2x^{2}-5\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}-5;}\underline{-x^{5}\phantom{-;x^n}+\frac{5}{2}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+\frac{5}{2}x^{3};}\frac{5}{2}x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-5-;x^n;}\underline{-2.5x^{3}\phantom{-;x^n}+\frac{25}{4}x\phantom{;}\phantom{-;x^n}}\\\phantom{;-2.5x^{3}+\frac{25}{4}x\phantom{;}-;x^n;}\frac{25}{4}x\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$
$\frac{1}{2}x^{3}+\frac{5}{4}x+\frac{\frac{25}{4}x-1}{2x^2-5}$
Risposta finale al problema
$\frac{1}{2}x^{3}+\frac{5}{4}x+\frac{\frac{25}{4}x-1}{2x^2-5}$