Question

Rezolva:
(x-1 - $\frac{x^{2} }{x+2}$ ) : $\frac{x-2}{x+2}$ =?

Answer 1

     
$[x -1 - \frac{x^2}{x+2}]: \frac{x-2}{x+2}= \\ \\ =[ \frac{(x -1)(x+2)}{x+2} - \frac{x^2}{x+2}]: \frac{x-2}{x+2}= \\ \\ =[ \frac{ x^{2} +x-2}{x+2} - \frac{x^2}{x+2}]: \frac{x-2}{x+2}= \\ \\ = \frac{ x^{2} +x-2- x^{2}}{x+2}: \frac{x-2}{x+2}= \\ \\ =\frac{x-2}{x+2}: \frac{x-2}{x+2}=\frac{x-2}{x+2}* \frac{x+2}{x-2}= \frac{(x-2)(x+2)}{(x-2)(x+2)}= \boxed{1}$