РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 164 (1-3)

164. Спростіть вираз: 1) y/〖yx-x〗^2 – y/〖yx+x〗^2 = y^(\y+x)/(x(y-x)) – y^(\y-x)/(x(y+x)) = (y^2+ xy- y^2+ xy)/(x(y-x)(y+x)) = 2xy/(〖x(y〗^2- x^2)) = 2y/(y^2- x^2 ); 2) 4x/(x^2- y^2 ) – (x+y)/〖xy-y〗^2 = 〖4x〗^(\y)/((x-y)(x+y)) – 〖x+y〗^(\x+y)/(y(x-y)) = 〖4xy-(x+y)〗^2/(y(x-y)(x+y)) = (〖4xy-(x〗^2+ 2xy+ y^2))/(y(x-y)(x+y)) = (〖4xy-x〗^2- 〖2xy-y〗^2)/(y(x-y)(x+y)) = (〖-x〗^2+ 2xy- y^2)/(y(x-y)(x+y)) = 〖-(x-y)〗^2/(y(x-y)(x+y)) = –(x-y)/(y(x+y)) = (y-x)/(y(x+y)); 3) 〖a-3〗^(\a(a-3))/(a+3) – 〖a+3〗^(\a(a+3))/(a-3) + 12^(\(a+3)(a-3))/a = (〖a(a-3)〗^2- 〖a(a+3)〗^2+ 〖12(a〗^2- 9))/(a(a-3)(a+3)) = (〖a(a〗^2- 6a+9)-a〖(a〗^2+ 6a+9)+ 〖12a〗^2- 108)/(〖a(a〗^2- 9)) = (a^3- 〖6a〗^2+ 9a- a^3- 〖6a〗^2- 9a+ 〖12a〗^2- 108)/(〖a(a〗^2- 9)) = – 108/(〖a(a〗^2- 9)) = 108/(〖a(9-a〗^2));