Question

Aflati x aparține lui Z pentru care 2x+4/z+1 aparține lui Z

Answer 1

$\dfrac{2x+4}{x+1} = \dfrac{2x+2+2}{x+1} = \dfrac{2(x+1)+2}{x+1} = \dfrac{2(x+1)}{x+1}+\dfrac{2}{x+1} = \\ \\ = \underset{\in \mathbb_{Z} }{2}+\dfrac{2}{x+1}\\\\ \dfrac{2}{x+1}\in \mathbb_{Z} \Rightarrow x+1 \in D_2 \Rightarrow x+1 \in \Big\{\pm1, \pm2 \Big\} \Rightarrow \\ \\ \Rightarrow x+1\in \Big\{-2,-1,1,2\Big\}\Big|-1 \Rightarrow \boxed{x\in \Big\{-3,-2,0,1\Big\}}$