已知(a-b)(b-c)(c-a)/(a+b)(b+c)(c+a)=5/132求(a/a+b)+(b/b+c)+(c/c+a)的值!401/264错误

Question

已知(a-b)(b-c)(c-a)/(a+b)(b+c)(c+a)=5/132求(a/a+b)+(b/b+c)+(c/c+a)的值!
401/264错误

Answer 1

由已知变形,得
(a-b)/(a+b)+(b-c)/(b+c)+(c-a)/(c+a)=5/132
-(a-b)/(a+b)-(b-c)/(b+c)-(c-a)/(c+a)=-5/132
(b-a)/(a+b)+(c-b)/(b+c)+(a-c)/(c+a)=-5/132
(b+a-2a)/(a+b)+(c+b-2b)/(b+c)+(a+c-2c)/(c+a)=-5/132
1-2a/(a+b)+1-2b/(b+c)+1-2c/(c+a)=-5/132
-2a/(a+b)-2b/(b+c)-2c/(c+a)=-5/132-3=-401/132
所以：a/(a+b)+b/(b+c)+c/(c+a)=401/264.