a) $\frac{2}{x-1}$ nguyên⇔(x-1)∈Ư(2)={±1;±2}
Nếu x-1=-1 ⇔ x= 0
Nếu x-1=1 ⇔ x= 2
Nếu x-1=-2 ⇔ x=-1
Nếu x-1=2 ⇔ x= 3
⇒x∈{-1;0;2;3}
b) $\frac{-6}{3x-2}$ nguyên ⇔(3x-2)∈{±1;±2;±3;±6}
c) $\frac{x-2}{x-1}$ = $1-\frac{1}{x-1}$ nguyên⇔ (x-1)∈{±1}
Khi x-1=-1⇔x=0
Khi x-1=1⇔x=2
Vậy x∈{0;2}
d)$\frac{2x+3}{x-5}$ =$2+\frac{13}{x-5}$ nguyên ⇔(x-5)∈Ư(13)={±1;±13}