\(\frac{3x+2}{4x-1}\)là số nguyên suy ra \(\frac{4\left(3x+2\right)}{4x-1}=\frac{12x+8}{4x-1}=\frac{12x-3+11}{4x-1}=3+\frac{11}{4x-1}\inℤ\)
\(\Leftrightarrow\frac{11}{4x-1}\inℤ\Leftrightarrow4x-1\inƯ\left(11\right)=\left\{-11,-1,1,11\right\}\)mà \(x\inℤ\)
\(\Rightarrow x\in\left\{0,3\right\}\).
Thử lại đều thỏa mãn.