Вправа 401 - 500 » 467

467. Спрости вираз. a) (x – y)–2(x2 – y2) = (x^2- y^2)/〖(x-y)〗^2 = ((x-y)(x+y))/((x-y)(x-y)) = (x+y)/(x-y); б) (a–3 – b–3)–1 – (a–3 + b–3)–1 = (1/a^3 – 1/b^3 )–1 – (1/a^3 + 1/b^3 )–1 = ((b^3- a^3)/(a^3 b^3 ))–1 – ((b^3+ a^3)/(a^3 b^3 ))–1 = (a^3 b^3)/(b^3- a^3 ) – (a^3 b^3)/(b^3+ a^3 ) = (a^3 b^3 (b^3+ a^3- b^3+ a^3))/(〖(b〗^3- a^3)(b^3+ a^3)) = (a^3 b^3 • 〖2a〗^3)/(b^6- a^6 ) = (〖2a〗^6 b^3)/(b^6- a^3 ).