[tex] \it \dfrac{19}{2x+3} \in \mathbb{Z} \Rightarrow 2x+3|19 \Rightarrow 2x+3 \in D_{19} \Rightarrow 2x+3\in\{-19, -1,\ 1,\ 19\}|_{-3}\Rightarrow
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\Rightarrow 2x \in\{-22,\ -4,\ -2,\ 16\}|_{:2} \Rightarrow x\in\{ -11,\ \ -2,\ \ -1,\ \ 8\} =A [/tex]
