# G is residually finite, how to show that A is H-separable?

Let $G=A^{\; *}_{H} A$ be the generalized free products amalgamating $H$. Let $G$ be residually finite. How to show that $A$ is $H$-separable?
I'm sure that $A$ must be $H$-separable. But I don't know how to show this.
I started with $x \in A \backslash H$.
Since $A$ is residually finite, then there exists $M \lhd_{f} A$ such that $x \notin M$.
I'm trying to prove by contradiction, by assuming $x \in HM$.