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Let $A$ be a domain with field of fractions $K$. Let $f, g \in A[X]$ with $g$ monic. Show that if $f/g \in K[X]$ then $f/g \in A[X]$.

So I tried the direct approach by just assuming $f/g$ has a coefficient $a/b$ and then multiplying out with $g$ with the purpose of getting that $f$ has an "irrational" coefficient; but I can't finisnh.

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