Question

F = \{ x e N | \frac { 2 x + 5 } { x + 1 } e N \}.

Answer 1

Explicație pas cu pas:

$\frac{2x + 5}{x + 1} = \frac{2x + 2 + 3}{x + 1} = \frac{2(x + 1) + 3}{x + 1} = 2 + \frac{3}{x + 1} \in \mathbb{N} \\ \implies \frac{3}{x + 1} \in \mathbb{N} \implies (x + 1) \in \mathcal{D}_{3} \\ \implies (x + 1) \in \Big\{ 1; 3 \Big\} \implies x  \in \Big\{ 0; 2 \Big\}$