$\text{Giải thích các bước giải:}$
$a, \dfrac{6x-1}{3x+2} ∈ Z$
$⇔ 6x - 1$ $\vdots$ $3x + 2$
$⇔ 2 × (3x + 2) - 5$ $\vdots$ $3x + 2$
$⇔ 5$ $\vdots$ $3x + 2$
$\text{⇔ 3x + 2 ∈ Ư(5) = {±1, ±5}}$
$\text{⇔ 3x ∈ {-1, -3, -7, 3}$
$⇔ x ∈ [\dfrac{-1}{3}, -1, \dfrac{-7}{3}, 1]$
$\text{Do x ∈ Z ⇒ x ∈ {±1}}$
$b, \dfrac{x}{2} - \dfrac{2}{y} = \dfrac{1}{2}$
$⇒ \dfrac{2}{y} = \dfrac{x}{2} - \dfrac{1}{2}$
$⇒ \dfrac{2}{y} = \dfrac{x-1}{2}$
$⇒ (x - 1)y = 4$
$\text{⇒ x - 1 , y ∈ Ư(4) = {±1, ±2, ±4}}$
$\text{⇒ (x,y) ∈ {(2,4); (0,-4); (5,1); (-3,-1); (3,2); (-1,-2)}}$
$\text{Chúc bạn học tốt !}$
