РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 160

160. Виконайте дії: 1) (y-2)/5 + (3+y)/5 + (1-y)/5 = (y-2+3+y+1-y)/5 = (y+2)/5; 2) a^3/(a-c) – c^3/(a-c) = (a^3- c^3)/(a-c) = ((a-c)(a^2+ ac+ c^2))/(a-c) = a2 + ac + c2; 3) 64/(a-4) – a^3/(a-4) = 〖64-a〗^3/(a-4) = (4^3- a^3)/(a-4) = –((4-a)(16+4a+ a^2))/(a-4) = –a2 – 4a – 16; 4) x/(x^3+ y^3 ) – y/(x^3+ y^3 ) = (x+y)/(x^3+ y^3 ) = (x+y)/(〖(x+y)(x〗^2- xy + y^2)) = 1/(x^2- xy + y^2 ); 5) (x^2+ y^2)/(x^3+ y^3 ) – xy/(x^3+ y^3 ) = (x^2+ y^2- xy)/(x^3 + y^3 ) = (x^2+ y^2- xy)/(〖(x+y)(x〗^2- xy + y^2)) = 1/(x+y); 6) ( y^2)/(x^3- y^3 ) + (xy+ x^2)/(x^3- y^3 ) = (y^2+ xy+ x^2)/(〖(x-y)(x〗^2+ xy + y^2)) = 1/(x-y).