Вправа 401 - 500 » 466

466. Спростіть вираз. a) (a–1 – c–1) : (a^2- c^2)/ac = (1/a – 1/c) • ac/(a^2- c^2 ) = (c-a)ac/(ac(a-c)(a+c)) = (-1)/(a+c); б) 1/(a^(-3)- x^(-3) ) – 1/(a^(-3)+ x^(-3) ) = 1/(1/a^3 - 1/x^3 ) – 1/(1/a^3 + 1/x^3 ) = (a^3 x^3)/(x^3- a^3 ) – (a^3 x^3)/(x^3+ a^3 ) = = (a^3 x^3 (x^3+ a^3- x^3+ a^3))/(〖(x〗^3- a^3)(x^3+ a^3)) = (a^3 x^3 • 〖2a〗^3)/(x^6- a^6 ) = (〖2a〗^6 x^3)/(x^6- a^6 ); в) (m–1 + n–1)2 + (m–1 – n–1)2 = (1/m + 1/n)2 + (1/m – 1/n)2 = 〖(n+m)〗^2/(m^2 n^2 ) + 〖(n-m)〗^2/(m^2 n^2 ) = (n^2+ 2mn+ m^2+ n^2- 2mn+ m^2)/(m^2 n^2 ) = (〖2n〗^2+ 〖2m〗^2)/(m^2 n^2 ).