Question

Determinati valorile intregi ale lui x,astfel incat 2x+5 supra x+2 sa fie numar intreg

Answer 1

[tex]\dfrac{2x+5}{x+2}=\dfrac{2x+4+1}{x+2}= \dfrac{2x+4}{x+2}+\dfrac{1}{x+2} = \dfrac{2(x+2)}{x+2}+\dfrac{1}{x+2} = \\\;\\ = 2+\dfrac{1}{x+2} \in \mathbb{Z} \Rightarrow x+2 \in \{-1, 1 \} \Rightarrow x\in \{-3, -1\}[/tex]