Question

Determinati elementele multimii A={x | x∈Z-{-1}, 3x+2/x+1∈Z}

Ajutati-ma va rog :D

Answer 1

[tex]A=\{x|x \in Z-\{1\}, \frac{3x+2}{x+1} \in Z \} \\ \frac{3x+2}{x+1} \in Z; \\ x+1|x+1|*3 ~\longrightarrow x+1|3x+3~(1) \\ x+1|3x+2 ~~~~\longrightarrow x+1|3x+2~(2) \\ (1)-(2) \longrightarrow x+1|1 \\ ~~~~~~~~~~~~~~~~~~~x+1 \in \{1;-1\}|-1 \\ ~~~~~~~~~~~~~~~~~~~x \in \{0;-2\} \Longrightarrow \boxed{A=\{0;-2\}}[/tex]