Вправа 301 - 400 » 308

308. Спростіть вираз. a) (x/y^2 – 1/x) : (1/x + 1/y) = (x^2- y^2)/〖xy〗^2 : (x+y)/xy = (〖(x〗^2- y^2)xy)/(〖xy〗^2 (x+y)) = ((x-y))/y; б) (a/b + a^2/b^2 ) : (b^2/a^2 + b/a) = 〖ab+a〗^2/b^2 : (b^2+ ab)/a^2 = 〖a(b+a)•a〗^2/(b^2 (b+a)b) = a^3/b^3 ; в) (m/(m+1) + 1) : (1 – 〖3m〗^2/〖1-m〗^2 ) = (m+m+1)/(m+1) : (1- m^2- 〖3m〗^2)/〖1-m〗^2 = (2m+1)/(m+1) • 〖1-m〗^2/〖1-4m〗^2 = (1-m)/(1-2m); г) ((3a+1)/(3a-1) – (3a-1)/(3a+1)) : 12a/(15a-5) = (〖(3a+1)〗^2- 〖(3a-1)〗^2)/(〖9a〗^2- 1) • (5(3a-1))/12a = ((3a+1-3a+1)(3a+1+3a-1)•5(3a-1))/((3a-1)(3a+1)•12a) = (5 •2 •6a)/(12a(3a+1)) = 5/(3a+1).