已知abc≠0,且a+b+c=0,则代数式a^2/bc+b^2/ac+c^2/ab的值为多少?

a+b+c=0,a+b=-ca^2/bc+b^2/ac+c^2/ab通分=(a^3+b^3+c^3)/abc=[(a+b)(a^2-ab+b^2)+c^3]/abc=[-c(a^2-ab+b^2)+c^3]/abc={-c[(a+b)^2-3ab]+c^3}/abc=[-c(c^2-3ab)+c^3]/abc=(-c^2+3abc+c^3)/abc=3abc/abc=3由a^3+b^3到(a+b)(a^2-ab+b^2)怎么变的a^3+b^3 =a^3-a^2b+ab^2+a^2b-ab^2+b^3(添项) =（a+b）a^2-ab(a+b)+(a+b)b^2(分组) =(a+b)(a^2-ab+b^2)