[latex]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} \ \ 1inmathbb{Z}Rightarrowfrac{4}{x-1}inmathbb{Z}Rightarrow (x-1)mid4 \ \ x-1in{1,2,4,-1,-2,-4} \ \ xin{2,3,5,0,-1,-3} \ \ A={2,3,5,0,-1,-3}[/latex]