如何证明a/c=b/d=(a-b)/(c-d)

证明如下：∵a/b = c/d∴a/b +1 = c/d + 1∴(a+b)/b = (c+d)/d∴b/(a+b) = d/(c+d)∴2b/(a+b) = 2d/(c+d)∴2b/(a+b)-1 = 2d/(c+d)-1∴{2b-(a+b)} /(a+b) = {2d-(c+d)} /(c+d)∴(b-a) /(a+b) = (d-c) /(c+d)∴-(b-a) /(a+b) = -(d-c) /(c+d)∴(a-b) /(a+b) = (c-d) /(c+d)∴(a+b)/(a-b)=(c+d)/(c-d)