soluzione Calcolare { 3a2 x+2a + [x2 : (1 - a x+a ) +a2 : (1 - x x+a )]: x2+2ax+a2 x-2a } : ( x2-a2 x2 : x2-4a2 x2 ) = = { 3a2 x+2a + [x2 : x+a-a x+a +a2 : x+a-x x+a ]: x2+2ax+a2 x-2a } : ( x2-a2 x2 : x2-4a2 x2 ) = = { 3a2 x+2a + [x2 : x x+a +a2 : a x+a ]: x2+2ax+a2 x-2a } : ( x2-a2 x2 : x2-4a2 x2 ) = = { 3a2 x+2a + [x2 · x+a x +a2 · x+a a ]: x2+2ax+a2 x-2a } : ( x2-a2 x2 · x2 x2-4a2 ) = = { 3a2 x+2a + [x(x+a) +a(x+a) ]: x2+2ax+a2 x-2a } : x2-a2 x2-4a2 = sup> = { 3a2 x+2a + [x2+ax+ax+a2]: x2+2ax+a2 x-2a } : x2-a2 x2-4a2 ) = = { 3a2 x+2a + [x2+2ax+a2]: x2+2ax+a2 x-2a } : x2-a2 x2-4a2 = = { 3a2 x+2a + [x2+2ax+a2]· x-2a x2+2ax+a2 } : x2-a2 x2-4a2 = = { 3a2 x+2a + (x+a)2 · x-2a (x+a)2 } : x2-a2 x2-4a2 = = { 3a2 x+2a + x - 2a } : x2-a2 x2-4a2 = = 3a2+(x+2a)(x-2a) x+2a : x2-a2 x2-4a2 = = 3a2+x2-4a2 x+2a : x2-a2 x2-4a2 = = x2-a2 x+2a · x2-4a2 x2-a2 = = (x-a)(x+a) x+2a · (x-2a)(x+2a) (x-a)(x+a) =   =   x-2a