已知a/b=c/d.求证:a+c/b+d=a-c/b-d

Answer 1

证明：
假设a/b = c/d = k
则a = kb,c= kd
所以(a+c) / (b+d)
= (kb + kd) / (b+d) = k(b+d) / (b+d) = k
(a-c) / (b-d)
= (kb-kd) / (b-d) = k(b-d) / (b-d) = k
因此
(a+c)/(b+d) = (a-c)/(b-d)