N° 6 Espressioni Algebriche

$\frac{2 x + 7}{x^{3} + 2 x^{2} - x - 2} - \frac{3}{x^{2} + x - 2} + \frac{2}{x^{2} + 3 x + 2} - \frac{1}{x^{2} - 1} =$

$= \frac{2 x + 7}{(x - 1) (x + 1) (x + 2)} - \frac{3}{(x - 1) (x + 2)} + \frac{2}{(x + 1) (x + 2)} - \frac{1}{(x + 1) (x - 1)} =$

$= \frac{2 x + 7 - 3 (x + 1) + 2 (x - 1) - (x + 2)}{(x - 1) (x + 1) (x + 2)} =$

$= \frac{2 x + 7 - 3 x - 3 + 2 x - 2 - x - 2}{(x - 1) (x + 1) (x + 2)} =$

$= \frac{(2 - 3 + 2 - 1) x + (7 - 3 - 2 - 2)}{(x - 1) (x + 1) (x + 2)} =$

$= \frac{0}{(x - 1) (x + 1) (x + 2)} = 0$