N° 12 Espressioni Algebriche

${(2 x + 2 y) \cdot (\frac{x^{2} - y^{2}}{x + y})}^{3} \cdot {(\frac{x^{2} - y^{2}}{x + y})}^{- 4} \cdot (1 + \frac{2 y}{x - y}) {[(1 - \frac{2 xy}{x^{2} + xy + y^{2}}) : \frac{x^{3} + y^{3}}{x^{3} - y^{3}}]}^{2} =$

$= 2 (x + y) \frac{{(x^{2} - y^{2})}^{3}}{{(x + y)}^{3}} \cdot \frac{{(x + y)}^{4}}{{(x^{2} - y^{2})}^{4}} \cdot (\frac{x - y + 2 y}{x - y}) \cdot {[(\frac{x^{2} + xy + y^{2} - 2 xy}{x^{2} + xy + y^{2}}) \cdot \frac{(x - y) (x^{2} + xy + y^{2})}{(x + y) (x^{2} - xy + y^{2})}]}^{2} =$

$= 2 (x + y) \cdot \frac{x + y}{x^{2} - y^{2}} \cdot (\frac{x + y}{x - y}) \cdot {(\frac{x^{2} - xy + y^{2}}{x^{2} + xy + y^{2}} \cdot \frac{(x - y) (x^{2} + xy + y^{2})}{(x + y) (x^{2} - xy + y^{2})})}^{2} =$

$= 2 \cdot \frac{{(x + y)}^{3}}{(x + y) {(x - y)}^{2}} \cdot \frac{{(x - y)}^{2}}{{(x + y)}^{2}} = 2$