If a = b - c, b = c - d, c = d - a, and abc*d ≠ 0, then what is the value of a/b + b/c + c/d + d/a?

a = b-c ---1
b = c-d ---2
c = d-a ---3

Add LHS and RHS
a+b+c = b-a
=>a+c = -a
=> c = -2a ---4

From 1,4 => b = -a
similarly,
c = -2a
d = -a

=>
a/b + b/c + c/d + d/a = 1/2
Answer: 1/2



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