Вправи 401 - 467 » 414

414. Знайдіть m/n, якщо: 1) (n^(-1)+ m^(-1))/(n^(-1)- m^(-1) ) = 3; (1/n+ 1/m)/(1/n- 1/m) = 3;((m+n)/mn)/((m-n)/mn) = 3; ((m+n)•mn)/(mn •(m-n)) = 3; (m+n)/(m-n) = 3; 3(m – n) = m + n; 3m – 3n = m + n; 3m – m = n + 3n; 2m = 4n |: 2n; m/n = 2. 2) (m^(-1)- 〖4n〗^(-1))/(〖3n〗^(-1)+ m^(-1) ) = 5; (1/m- 4/n)/(3/n+ 1/m) = 5; ((n-4m)/mn)/((3m+n)/mn) = 5; ((n-4m)•mn)/(mn(3m+n)) = 5; (n-4m)/(3m+n) = 5. 5(3m + n) = n – 4m; 15m + 5n = n – 4m; 15m + 4m = n – 5n; 19m = –4n |: 19n; m/n = –4/19.