Вправа 201 - 300 » 279

279. Виконай ділення. a) (〖16xy〗^2- x^3)/(x^2- 2xy+ y^2 ) : (x^2 y- 〖16y〗^3)/(x^2- y^2 ) = (〖x(16y〗^2- x^2)(x^2- y^2))/(〖(x-y)〗^2 •y • 〖(x〗^2- 16y^2)) = (-x(x+y))/(y(x-y)) = (x(x+y))/(y(y-x)); б) (x^2+ 2xy+ y^2)/(y^2 x- 〖9x〗^3 ) : (x^2- y^2)/(〖9x〗^2 y- y^3 ) = (〖(x+y)〗^2 •y • 〖(9x〗^2- y^2))/(x〖(y〗^2- 〖9x〗^2) •(x^2- y^2)) = (-y(x+y))/(x(x-y)) = (y(x+y))/(x(y+x)); в) (x^2+ xy)/(〖5x〗^2- 〖5y〗^2 ) : (x^2 xy)/(x^3+ y^3 ) = (x(x+y))/(5(x^2- y^2)) • ((x+y)(x^2- xy+ y^2))/(x(x-y)) = (x^3+ y^3)/(5(x- 〖y)〗^2 ); г) (x^2- 2xy)/(x^2+ 〖4y〗^2 ) : 〖(x-2y)〗^2/(x^4- 〖16y〗^4 ) = (x(x-2y)• 〖(x〗^2- 〖4y〗^2)(x^2+ 〖4y〗^2))/(〖(x〗^2+ 〖4y〗^2) •(x- 〖2y)〗^2 ) = (x〖(x〗^2- 〖4y〗^2))/(x-2y) = x(x + 2y).