Вправа 301 - 400 » 309

309. Спростіть вираз. а) (a- b)/a • (a/(a- b) + a/b) = (a- b)/a • (ab+ a^2- ab)/(b(a- b)) = (a- b)/a • a^2/((a- b)b) = a/b; б) (x/y – x/(x+ y)) • (x+ y)/x = (x^2+ xy- xy)/(y(x+ y)) • (x+ y)/x = x^2/y • 1/x = x/y; в) ((x+ y)/(x- y) + (x- y)/(x+ y)) : 2/(x^2-y^2 ) = (〖(x+ y)〗^2+ 〖(x- y)〗^2)/(x^2- y^2 ) • (x^2- y^2)/2 = (x^2+2xy+ y^2+x^2-2xy+y^2 )/1 • 1/2 = (〖2x〗^2+ 〖2y〗^2)/2 = x2 + y2; г) ((a- b)/(a+ b) – (a+ b)/(a- b)) : 4/(a^2-b^2 ) = (〖(a- b)〗^2-〖(a+ b)〗^2 )/(a^2- b^2 ) • (a^2- b^2)/4 = (a^2-2ab+b^2-a^2-2ab- b^2 )/4 = –ab.