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Indeed, because

P(A,B,C)/P(C) = P(A,B,C)/P(B,C).P(B,C)/P(C) 

$$ \frac{P(A,B,C)}{P(C)} = \frac{P(A,B,C)}{P(B,C)}\frac{P(B,C)}{P(C)} $$

Indeed, because

P(A,B,C)/P(C) = P(A,B,C)/P(B,C).P(B,C)/P(C) 

Indeed, because

$$ \frac{P(A,B,C)}{P(C)} = \frac{P(A,B,C)}{P(B,C)}\frac{P(B,C)}{P(C)} $$

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Indeed, because

P(A,B,C)/P(C) = P(A,B,C)/P(B,C).P(B,C)/P(C)