Вправи 201 - 300 » 229

229. Спростіть вираз: 1) (〖16a〗^2 b^2)/5xy : 〖12ab〗^3/(〖25x〗^2 y^3 ) • 〖3a〗^2/4y = (〖16a〗^2 b^2)/5xy • (〖25x〗^2 y^3)/〖12ab〗^3 • 〖3a〗^2/4y = (〖16a〗^2 b^2• 〖25x〗^2 y^3•〖3a〗^2 )/(5xy• 〖12ab〗^3•4y) = (〖20a〗^4 b^2 x^2 y^3)/(〖4ab〗^3 〖xy〗^2 ) = (〖5a〗^3 xy)/b; 2) (x^2+y^2+2xy )/(x^3- y^3 ) : (x^2-y^2 )/(xy+x^2+y^2 ) = (x^2+y^2+2xy )/(x^3- y^3 ) • (〖xy+ x〗^2+ y^2)/(x^2- y^2 ) = (〖(x〗^2+y^2+2xy)•(xy+x^2+y^2) )/(〖(x〗^3- y^3)• 〖(x〗^2- y^2)) = (〖(x〗^2+2xy+y^2)• 〖(x〗^2+ xy+y^2) )/((x- y) 〖(x〗^2+ xy+ y^2)•(x- y)(x+ y)) = 〖(x+ y)〗^2/(〖(x- y)〗^2 (x+ y)) = (x+ y)/〖(x- y)〗^2 .