Question

Ajutor va rog.Explicatie pas cu pas.​

Answer 1

Explicație pas cu pas:

x - 1 ≠ 0 => x ≠ 1

$\dfrac{x + 2}{x - 1} = \dfrac{(x - 1) + 3}{x - 1} = \dfrac{x - 1}{x - 1} + \dfrac{3}{x - 1} = 1 + \dfrac{3}{x - 1} \in \mathbb{N} \\ \implies \dfrac{3}{x - 1} \in \mathbb{N} \implies (x - 1) \in \mathcal{D}_{3} \\ \implies (x - 1) \in \Big\{ 1; 3 \Big\} \implies x \in \Big\{ 2; 4 \Big\}$

$\iff A = \Big\{ 2; 4 \Big\}$

$- 1 \leqslant \dfrac{4x - 6}{2} < 5 \\ - 2 \leqslant 4x - 6 < 10 \\ 4 \leqslant 4x < 16 \\ 1 \leqslant x < 4 \implies B = \Big[1 ; 4 \Big)$

=>

$A \cap B = \Big\{ 2; 4 \Big\} \cap \Big[1 ; 4 \Big) = \Big\{ 2 \Big\}$