[tex] \displaystyle\\
A=\left\{x\in Z \Big| \frac{2x+1}{x-1} \in Z \right\}\\\\
\frac{2x+1}{x-1}=\frac{2x -2+2+1}{x-1}=\frac{2x -2+3}{x-1}=\\\\
=\frac{2x -2}{x-1}+\frac{3}{x-1}=\frac{2(x -1)}{x-1}+\frac{3}{x-1}=2+\frac{3}{x-1}\\\\
2\in Z\\\\
\text{Ne ocupam de: }~~\frac{3}{x-1}\\\\
\frac{3}{x-1} \in Z\\\\
\Rightarrow~~(x-1) \in D_3\\\\
D_3= \{-3;~-1;~1;~3\}\\\\
x-1 = -3 ~=\!\!>~x = -3+1=-2\\
x-1 = -1 ~=\!\!>~x = -1+1=0\\
x-1 = 1 ~=\!\!>~x = 1+1=2\\
x-1 = 3 ~=\!\!>~x = 3+1=4\\\\
\boxed{A=\{-2;~0;~2;~4\}} [/tex]
