Задачі підвищеної складностістр » 4 (1)

6) (x^(-1)-y^(-1) )/(x^(-3)- y^(-3) ) : ( x^2 y^2)/((x+ y)^2-3xy) • ((x^2-y^2 )/xy)–1 = –xy/((x+ y)^2 ). 1. (x^(-1)-y^(-1))/(x^(-3)- y^(-3) ) = (1/x-1/y)/(1/x^3 + 1/y^3 ) = ((y- x)/xy)/((y^3+x^3)/(x^3 y^3 )) = ((y- x) x^3 y^3)/(xy(y^3 + x^3)) = ((y- x) x^2 y^2)/(y^3+ x^3 ); 2. (x^2 y^2)/((x+ y)^2-3xy) = (x^2 y^2)/(x^2+ 2xy+ y^2-3xy) = (x^2 y^2)/(x^2-xy+ y^2 ); 3. ((y- x)x^2 y^2)/(y^3+ x^3 ) : (x^2 y^2)/(x^2- xy+ y^2 ) • ((x^2-y^2)/xy)–1 = ((y- x)x^2 y^2 (x^2 - xy+ y^2))/((y+ x)(x^2 - xy+ y^2 ) •〖 x〗^2 y^2 ) • xy/((x- y)(x+ y)) = –xy/((x+ y)^2 ).