Matematică
sebi04
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Determinati numerele intregi x pentru care: [latex] \frac{2x+1}{x-1} [/latex]∈Z *Dau coroana*

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marianatapu

[latex]\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\}[/latex]

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