Gọi \(d\)là \(UCLN\left(2n+3;4n+8\right)\)
\(\Rightarrow\left\{{}\begin{matrix}2n+3⋮d\\4n+8⋮d\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}4n+6⋮d\\4n+8⋮d\end{matrix}\right.\)
\(\Rightarrow\left(4n+8\right)-\left(4n+6\right)⋮d\)
\(2⋮d\)
\(\Rightarrow\dfrac{2n+3}{4n+8}\) tối giản khi và chỉ khi \(n\in\left\{\pm1;\pm2\right\}\)