РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 165

165. Виконайте дії: 1) 〖4y-2〗^(\35)/15 + 〖3+3y〗^(\21)/25 + 〖1-3y〗^(\15)/35 = (140y-70+63+63y+15-45y)/525 = (158y+8)/525; 2) y/〖xy-x〗^2 + x/〖xy-y〗^2 = y/(x(y-x)) + x/(y(x-y)) = y^(\y)/(x(y-x)) – x^(\x)/(y(y-x)) = (y^2- x^2)/(xy(y-x)) = ((y-x)(y+x))/(xy(y-x)) = (y+x)/xy; 3) (1-t)/(t^2- t) – (t+1)/〖1-t〗^2 = (1-t)/(t(t-1)) – (t+1)/((1-t)(1+t)) = –(t-1)/(t(t-1)) + 1/(t-1) = –1^(\t-1)/t + 1^(\t)/(t-1) = (-t+1+t)/(t(t-1)) = 1/(t(t-1)); 4) 4/(t^2- 9) – 2/(t^2+ 3t) = 4^(\t)/((t-3)(t+3)) – 2^(\t-3)/(t(t+3)) = (4t-2t+6)/〖t(t-3)(t+3)〗^2 = (2t+6)/〖t(t-3)(t+3)〗^2 = (2(t+3))/〖t(t-3)(t+3)〗^2 = 2/(t(t-3)(t+3)) = 2/(〖t(t〗^2- 9)).