Question

Como fatorar x3-1/x2-x

Answer 1

$\textbf{Diferen\c{c}a de cubos:}\\\\ \mathrm{x^3-y^3=(x-y)(x^2+xy+y^2)}\\\\ \textbf{Fatorando a express\~ao:}\\\\ \mathrm{\dfrac{x^3-1}{x^2-x}=\dfrac{x^3-1^3}{x.x-x.1}=\dfrac{(x-1)(x^2+x+1)}{x(x-1)}=}\\\\ \mathrm{=\boxed{\mathbf{\dfrac{x^2+x+1}{x}}}}$