Răspuns:
C = {1}
Explicație pas cu pas:
[tex]\frac{3x + 2}{2x + 3}\in \mathbb{N} \\ [/tex]
(2x + 3) divide pe (3x + 2) =>
[tex](2x + 3) \ \Big| \ (2x + 3) | \cdot 3 \implies \ (2x + 3) \ \Big| \ (6x + 9)\\ (2x + 3) \ \Big| \ (3x + 2) | \cdot 2 \implies (2x + 3) \ \Big| \ (6x + 4)\\ [/tex]
=> (2x + 3) divide și diferența:
[tex](2x + 3) \ \Big| (6x + 9 - 6x - 4) \implies (2x + 3) \ \Big| 5 \\ \implies (2x + 3) \in \{1; 5\} \Big|_{-3} \implies 2x \in \{-2;2\} \Big|_{:2} \\ \implies x \in \{-1;1\} \cap \mathbb{N} \implies \bf x = 1[/tex]
=> C = {1}
