Question

$\frac{ x^{3}+ 2x^{2}-x-2 }{2+x(x+3)}$ Aratati ca raportul este un numar intreg pentru care x aprtine Z

Answer 1

$=\dfrac{x^2(x+2)-(x+2)}{x^2+3x+2}=\dfrac{(x+2)(x^2-1)}{x^2+x+2x+2}=\dfrac{(x+2)(x+1)(x-1)}{x(x+1)+2(x+1)}= \\ \\ \\ =\dfrac{(x+2)(x+1)(x-1)}{(x+1)(x+2)}=x-1$