\(\frac{2x+3}{x-1}=\frac{2\left(x-1\right)+5}{x-1}=\frac{2\left(x-1\right)}{x-1}+\frac{5}{x-1}=2+\frac{5}{x-1}\in Z\)
\(\Rightarrow5⋮x-1\)
\(\Rightarrow x-1\inƯ\left(5\right)=\left\{1;-1;5;-5\right\}\)
\(\Rightarrow x\in\left\{2;0;6;-4\right\}\)
Vì x nguyên bé nhất
\(\Rightarrow x=-4\)