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To solve the problem, let's assume the common setup where we have the equations:

Given:
(a + \frac{1} = 1) and (b + \frac{1}{c} = 1)

Find: (c + \frac{1}{a})

Step 1: Express (a) in terms of (b)

From (a + \frac{1} = 1):
(a = 1 - \frac{1} = \frac{b - 1})

Thus, (\frac{1}{a} = \frac{b - 1})

Step 2: Express (c) in terms of (b)

From (b + \frac{1}{c} = 1):
(\frac{1}{c} = 1 - b)

Thus, (c = \frac{1}{1 - b})

Step 3: Calculate (c + \frac{1}{a})

(c + \frac{1}{a} = \frac{1}{1 - b} + \frac{b - 1})

Rewrite (\frac{b - 1}) as (-\frac{1 - b}):
(= \frac{1}{1 - b} - \frac{1 - b})

Combine terms:
(= \frac{1 - b}{1 - b} = 1)

Answer: (\boxed{1})

If the problem refers to (\abc) (another common variant), the answer would be (-1). But based on typical questions, the most likely answer is 1.

(\boxed{1})

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