Задачі підвищеної складностістр » 5

((2- y)/(y-1) + (2(x-1))/(x-2)) : ((y(x-1))/(y-1) + (x(2- y))/(x-2)). 1. (2- y)/(y-1) + (2(x-1))/(x-2) = (2x- xy-4+2y+2xy-2x-2y+2)/((y-1)(x-2)) = (xy-2)/((y-1)(x-2)); 2. (y(x-1))/(y-1) + (x(2- y))/(x-2) = (y(x^2-3x+2)+ x(3y-2- y^2))/((y-1)(x-2)) = (yx^2-3xy+2y+3xy-2x- xy^2)/((y-1)(x-2)) = (yx^2+2y-2x- xy^2)/((y-1)(x-2)) = (xy(x- y)-2(x- y))/((y-1)(x-2)) = ((x- y)(xy-2))/((y-1)(x-2)); 3. (xy-2)/((y-1)(x-2)) : ((x- y)(xy-2))/((y-1)(x-2)) = ((xy-2)(y-1)(x-2))/((y-1)(x-2)(x- y)(xy-2)) = 1/(x- y), що й треба було довести.