证明：（a-b/a+b）+（b-c/b+c）+（c-a/c+a）+(a-b)(b-c)(c-a)/(a+b)(b+c)(c+a)=0

Question

证明：（a-b/a+b）+（b-c/b+c）+（c-a/c+a）+(a-b)(b-c)(c-a)/(a+b)(b+c)(c+a)=0

Answer 1

设：x=a+b,y=b+c,m=c+a 则a-b=m-y,b-c=x-m,c-a=y-x (a-b)/(a+b)=(m-y)/x (b-c)/(b+c)=(x-m)/y (c-a)/(c+a)=(y-x)/m得：原式= (m-y)/x +(x-m)/y+ (y-x)/m+(m-y)(x-m)(y-x)/(xym) 　　= (my-y²+x²-mx)/(xy) ...