Esercizio
$\frac{40x^4-x^3+3\:}{4x^2-3}$
Soluzione passo-passo
1
Dividere $40x^4-x^3+3$ per $4x^2-3$
$\begin{array}{l}\phantom{\phantom{;}4x^{2}-3;}{\phantom{;}10x^{2}-\frac{1}{4}x\phantom{;}+\frac{15}{2}\phantom{;}\phantom{;}}\\\phantom{;}4x^{2}-3\overline{\smash{)}\phantom{;}40x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x^{2}-3;}\underline{-40x^{4}\phantom{-;x^n}+30x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-40x^{4}+30x^{2};}-x^{3}+30x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}-3-;x^n;}\underline{\phantom{;}x^{3}\phantom{-;x^n}-\frac{3}{4}x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}-\frac{3}{4}x\phantom{;}-;x^n;}\phantom{;}30x^{2}-\frac{3}{4}x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}-3-;x^n-;x^n;}\underline{-30x^{2}\phantom{-;x^n}+\frac{45}{2}\phantom{;}\phantom{;}}\\\phantom{;;-30x^{2}+\frac{45}{2}\phantom{;}\phantom{;}-;x^n-;x^n;}-\frac{3}{4}x\phantom{;}+\frac{51}{2}\phantom{;}\phantom{;}\\\end{array}$
$10x^{2}-\frac{1}{4}x+\frac{15}{2}+\frac{-\frac{3}{4}x+\frac{51}{2}}{4x^2-3}$
Risposta finale al problema
$10x^{2}-\frac{1}{4}x+\frac{15}{2}+\frac{-\frac{3}{4}x+\frac{51}{2}}{4x^2-3}$