[tex]\dfrac{2x+5}{x+3}\in \mathbb{Z}\\ \\ \\\Rightarrow\,\dfrac{2(x+3)-1}{x+3} = \dfrac{2(x+3)}{x+3}-\dfrac{1}{x+3} = 2-\dfrac{1}{x+3} \in \mathbb{Z}\\ \\ \Rightarrow \,x+3 \,\,|\,\,1 \,\Leftrightarrow \,x+3\in D_1\,\Leftrightarrow \,x+3\in \{-1,1\}\Big|-3 \\ \\ \Leftrightarrow\, x \in \{-4,-2\}[/tex]
