[tex]\it \dfrac{2x+3}{x+2} \in\mathbb{Z} \Rightarrow x+2|2x+3 \ \ \ (1)
\\\;\\ \\\;\\
Dar,\ x+2|x+2 \Rightarrow x+2|2(x+2) \Rightarrow x+2|2x+4 \ \ \ (2)
\\\;\\ \\\;\\
(1),\ (2) \Rightarrow x+2|2x+4-2x-3 \Rightarrow x+2|1 \Rightarrow x+2 \in \{-1,\ 1\}|_{-2} [/tex]
[tex]\it \Rightarrow x\in \{-3,\ -1\} \Rightarrow A = \{-3,\ -1\}
\\\;\\ \\\;\\
A \cap [-3,\ -1) = \{-3,\ -1\} \cap [-3,\ -1) = \{-3\}[/tex]
