Gọi \(d=ƯCLN\left(12n+1;30n+2\right)\)
\(\Rightarrow\hept{\begin{cases}12n+1⋮d\\30n+2⋮d\end{cases}\hept{\begin{cases}5\left(12n+1\right)⋮d\\2\left(30n+2\right)⋮d\end{cases}\hept{\begin{cases}60n+5⋮d\\60n+4⋮d\end{cases}}}}\)
\(\Rightarrow\left(60n+5\right)-\left(60n-4\right)⋮d\)
\(\Rightarrow1⋮d\Leftrightarrow d=1\)
\(\Rightarrow\frac{12n+1}{30n+2}\)là phân số tối giản
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