Let $Q$ be a prime ideal of an integral domain $A$. Is $A[X]_{Q[X]}$ some localisation of $A_Q[X]$ ?

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Let $A$ be an integral domain and $Q$ be a prime ideal of $A$. Then $Q[X]$is a prime ideal of $A[X]$. My question is : Is $A[X]_{Q[X]}$ some localisation of $A_Q[X]$ ?