Вправи 201 - 300 » 231

230. Спростіть вираз: 1) (x^3+y^3 )/(x- y) : (x+ y)/(x^3-y^3 ) = (x^3+y^3 )/(x- y) • (x^3-y^3 )/( x+ y) = ((x^3+y^3)• 〖(x〗^3-y^3) )/((x- y)(x+ y)) = (x^6- y^6)/(x^2- y^2 ) = (〖(x〗^2 )^3-〖(y〗^2 )^3 )/(x^2-y^2 ) = (〖(x〗^2-y^2)〖(x〗^4+x^2 y^2+y^4) )/(x^2- y^2 ) = x4 + x2y2 + y4; 2) (a^2+ ab)/(a^2+b^2 ) : (a^2+2ab+b^2 )/(a^4-b^4 ) = (a^2+ ab)/(a^2+b^2 ) • (a^4-b^4 )/(a^2+2ab+b^2 ) = (〖(a〗^2+ ab)(a^4-b^4) )/(〖(a〗^2+ b^2)〖(a〗^2+2ab+ b^2)) = (a(a+ b) 〖(a〗^2-b^2)( a^2+b^2) )/(〖(a〗^2+ b^2)(〖a+ b)〗^2 ) = (a(a- b)(a+ b))/(a+ b) = a(a – b).