Вправи 201 - 300 » 232

231. Спростіть вираз: 1) (x^4-y^4 )/(x^2+y^2-2xy ) : (y+ x)/〖(x- y)〗^2 = (x^4-y^4 )/(x^2-2xy+y^2 ) + 〖(x- y)〗^2/(y+ x) • (〖(x〗^4-y^4)•〖(x- y)〗^2 )/(〖(x〗^2-2xy+y^2)•(x+ y) ) = (〖(x〗^2- y^2)〖(x〗^2+y^2)〖(x- y)〗^2 )/(〖(x- y)〗^2•(x+ y)) = ((x- y)(x+ y)(x^2+y^2) )/(x+ y) = (x – y)(x2 + y2); 2) (a^2+b^2- ab )/(x^2- y^2 ) : (a^3+b^3 )/(x^2+y^2-2xy ) = (a^2- ab+b^2 )/(x^2- y^2 ) • (x^2-2xy+y^2 )/(a^3+ b^3 ) = (〖(a〗^2- ab+b^2)•〖(x〗^2-2xy+y^2) )/(〖(x〗^2- y^2)(a^3+ b^3)) = (〖(a〗^2- ab+b^2)(〖x- y)〗^2 )/((x- y)(x+ y)(a+ b) 〖(a〗^2- ab+b^2) ) = (x- y)/((x+ y)(a+ b)).