[tex]\it \dfrac{3x-5}{x-1} \in\ \mathbb{Z} \Rightarrow x-1|3x-5 \ \ \ \ (1)[/tex]
[tex]\it x-1|x-1 \Rightarrow x-1|3(x-1) \Rightarrow x-1|3x-3\ \ \ (2)[/tex]
Din relațiile (1), (2), rezultă:
[tex]\it x-1|3x-3-(3x-5) \Rightarrow x-1|3x-3-3x+5 \Rightarrow x-1|2\Rightarrow [/tex]
[tex]\it \Rightarrow x-1\in D_2 \Rightarrow x-1 \in \{\pm1,\ \pm2\} \Rightarrow x-1 \in\{-2,\ -1,\ 1,\ 2\}|_{+1} [/tex]
[tex]\it \Rightarrow x\in\{ -1,\ 0,\ 2,\ 3\}[/tex]
Deci, A = {-1, 0, 2, 3}
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[tex]\it \dfrac{3x-5}{x-1}= \dfrac{3x-3-2}{x-1} =\dfrac{3(x-1)-2}{x-1} = 3-\dfrac{2}{x-1}\in\ \mathbb{Z} \Rightarrow x-1|2[/tex]
[tex]\it \Rightarrow x-1\in D_2 \Rightarrow x-1 \in \{\pm1,\ \pm2\} \Rightarrow x-1 \in\{-2,\ -1,\ 1,\ 2\}|_{+1} [/tex]
[tex]\it \Rightarrow x\in\{ -1,\ 0,\ 2,\ 3\}[/tex]
Deci, A = {-1, 0, 2, 3}
