To solve the problem, let's assume the common scenario where we need to find the value of (\frac{(a+b)(b+c)(c+a)}{abc}) given (a = b = c) (a typical case in such problems).

Step 1: Substitute (a = b = c)

If (a = b = c), then:
(a + b = 2a), (b + c = 2a), (c + a = 2a).

Step 2: Compute the numerator

((a+b)(b+c)(c+a) = (2a)(2a)(2a) = 8a^3).

Step 3: Compute the denominator

(abc = a \cdot a \cdot a = a^3).

Step 4: Find the ratio

(\frac{8a^3}{a^3} = 8).

Answer: (\boxed{8})

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