很简单：a(1/b+1/c)+b(1/a+1/c)+c(1/b+1/a)=a(b+c)/bc+b(a+c)/ac+c(a+b)/ab根据a+b+c=0有b+c=-a,a+c=-b,a+b=-c得：a(b+c)/bc+b(a+c)/ac+c(a+b)/ab = -(a^3+b^3+c^3)/abc= -((a+b)(a^2-ab+b^2)+c^3)/abc=-(-c*(a^2-ab...