Question

已知a+b+c=0,化简a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b).

Answer 1

a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b) =a(b+c)/(bc)+b(c+a)/(ca)+c(a+b)/(ab) =-a^2/(bc)-b^2/(ca)-c^2/(ab) =-(a^3+b^3+c^3)/(abc) =-((a+b+c)(a^2+b^2+c^2-ab-bc-ca)+3abc)/(abc) =-3abc/(abc) =-3