Question

Determinati numerele intregi x pentru care:
$\frac{2x+1}{x-1}$∈Z

*Dau coroana*

Answer 1

[tex]\frac{2x+1}{x-1} \in Z\\ \frac{2x+1}{x-1}=\frac{2(x-1)+3}{x-1}=2+\frac{3}{x-1}\\ 2\in Z\Rightarrow \frac{3}{x-1} \in Z\\ x-1\in D_3\\ x-1\in \{-3,-1,1,3\}\\ x\in \{-2,0,2,4\}\\ S:x\in \{-2,0,2,4\}[/tex]