Вправа 301 - 400 » 305

305. Виконай дії. а) (х+2)/(х+3) : (5х+10)/〖9-х〗^2 – (2х-1)/15 = (〖(х+2)•(9-х〗^2))/((х+3)•5(х+2)) – (2х-1)/15 = ((3-х))/5 – (2х-1)/15 = (9-3х-2х+1)/15 = (10-5х)/15 = (5(2-х))/15 = (2-х)/3; б) (6y/(y-4) – 3y) : (6-y)/(y-4) = (6y- 〖3y〗^2+ 12y)/(y-4) • (y-4)/(6-y) = 〖18y-3y〗^2/(6-y) = (3y(6-y))/(6-y) = 3y; в) (x^2- y^2)/〖(x-y)〗^2 • x^2/(x+y) + 〖1-x〗^2/(x-y) = (x+y)/(x-y) • x^2/(x-y) + 〖1-x〗^2/(x-y) = x^2/(x-y) + 〖1-x〗^2/(x-y) = (x^2+ 1- x^2)/(x-y) = 1/(x-y); г) (5-m)/(5+m) • (m + 〖2m〗^2/(5-m)) = (5-m)/(5+m) • ((5m- m^2+ 〖2m〗^2)/(5-m)) = ((5-m)• 〖(5m+m〗^2))/((5+m)•(5-m)) = (m(5+m))/(m+5) = m.