Задача из олимпиады

xy-x-y+1 = (x-1)(y-1) > 0;1/(xy)-1/x-1/y+1 = (1/x-1)(1/y-1) > 0;x+y+1/(xy)-(1/x+1/y+xy) = (1/(xy)-1/x-1/y+1) - (xy-x-y+1) = (1/x-1)(1/y-1) - (x-1)(y-1) = (x-1)(y-1)[1/xy-1] < 0.