Question

Aflati elementele multimii A.
A={x apartine Z| x+3/x-1 apartine Z}

Answer 1

$\frac{x+3}{x-1}=\frac{x-1+4}{x-1}=\frac{x-1}{x-1}+\frac{4}{x-1}=1+\frac{4}{x-1} \\ \\ 1\in\mathbb{Z}\Rightarrow\frac{4}{x-1}\in\mathbb{Z}\Rightarrow (x-1)\mid4 \\ \\ x-1\in\{1,2,4,-1,-2,-4\} \\ \\ x\in\{2,3,5,0,-1,-3\} \\ \\ A=\{2,3,5,0,-1,-3\}$