Gọi \(ƯC\left(3n+2;2n+1\right)\)là \(d\) \(\Leftrightarrow\left\{{}\begin{matrix}3n+2⋮d\\2n+1⋮d\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2\left(3n+2\right)⋮d\\3\left(2n+1\right)⋮d\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}6n+4⋮d\\6n+3⋮d\end{matrix}\right.\) \(\Leftrightarrow6n+4-\left(6n+3\right)⋮d\) \(\Leftrightarrow6n+4-6n-3⋮d\) \(\Leftrightarrow1⋮d\) \(\Leftrightarrow d=\pm1\) Vậy \(\dfrac{3n+2}{2n+1}\) là phân số tổi giản \(\forall\) \(n\in Z\) Chúc bạn học tốt!