Question

simplifique (y^4 -1) / (y^3-y^2+y-1)

Answer 1

$\displaystyle \frac{\text y^4-1}{\text y^3 - \text y^2 + \text y - 1}$

Numerador :

$\text y^4-1 \to (\text y^2+1)(\text y^2-1) = (\text y^2+1)(\text y-1)(\text y+1)$

$\displaystyle \frac{(\text y^2+1)(\text y^2-1)}{\text y^3-\text y^2+ \text y - 1} \to \frac{(\text y^2+1)(\text y-1)(\text y+1)}{\text y^3-\text y^2+ \text y - 1}$

No denominador vamos colocar o y² em evidência para os 2º termos :

$\displaystyle \frac{(\text y^2+1)(\text y-1)(\text y+1)}{\text y^2(\text y-1)+ \text y - 1}$

Colocando o (y-1) em evidência :

$\displaystyle \frac{(\text y^2+1)(\text y-1)(\text y+1)}{(\text y-1)(\text y^2 +1)}$

simplificando :

$\huge\boxed{\text y+1}$