Question

valorile intregi ale lui 6/x-2 apartine lui Z

Answer 1

[tex]\it \dfrac{6}{x-2}\in\mathbb{Z} \Rightarrow x-2|6 \Rightarrow x-2 \in D_6 \Rightarrowx-2\in\{\pm1,\ \pm2,\ \pm3,\ \pm6\} \Rightarrow \\\;\\ \\\;\\ \Rightarrow x-2 \in\{-6,\ -3,\ -2,\ -1,\ 1,\ 2,\ 3,\ 6\}|_{+2} \Rightarrow \\\;\\ \\\;\\ \Rightarrow x \in \{-4,\ -1,\ 0,\ 1,\ 3,\ 4,\ 5,\ 8\}[/tex]