a, \(\frac{3n-2}{4n-3}\)
Gọi d = ƯCLN(3n - 2, 4n - 3)
\(\Rightarrow\left\{{}\begin{matrix}3n-2⋮d\\4n-3⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3\left(3n-2\right)⋮d\\2\left(4n-3\right)⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}9n-6⋮d\\8n-6⋮d\end{matrix}\right.\)
\(\Rightarrow\) 9n - 6 - 8n + 6 \(⋮\) d
\(\Rightarrow\) 1 \(⋮\) d
\(\Rightarrow\) d = 1
\(\Rightarrow\) ƯCLN(3n - 2, 4n - 3) = 1
Vậy phân số \(\frac{3n-2}{4n-3}\) tối giản
b, \(\frac{4n+1}{6n+1}\)
Gọi d = ƯCLN(4n + 1, 6n + 1)
\(\Rightarrow\left\{{}\begin{matrix}4n+1⋮d\\6n+1⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3\left(4n+1\right)⋮d\\2\left(6n+1\right)⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}12n+3⋮d\\12n+2⋮d\end{matrix}\right.\)
\(\Rightarrow\) 12n + 3 - 12n - 2 \(⋮\) d
\(\Rightarrow\) 1 \(⋮\) d
\(\Rightarrow\) d = 1
\(\Rightarrow\) ƯCLN(4n + 1, 6n + 1) = 1
Vậy phân số \(\frac{4n+1}{6n+1}\) tối giản
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