Gọi \(d=ƯCLN\left(2m+9;14m+62\right)\) (\(d\in N\)*)
\(\Leftrightarrow\left\{{}\begin{matrix}2m+9⋮d\\14m+62⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}14m+63⋮d\\14m+62⋮d\end{matrix}\right.\)
\(\Leftrightarrow1⋮d\)
Vì \(d\in N\)*;\(1⋮d\Leftrightarrow d=1\)
\(\LeftrightarrowƯCLN\left(2m+9;14m+62\right)=1\)
\(\Leftrightarrow x=\dfrac{2m+9}{14m+62}\) tối giản với mọi n
Gọi d là UCLN(2m+9;14m+62)
\(\Leftrightarrow2m+9⋮d\Rightarrow7\left(2m+9\right)⋮d\Rightarrow14m+63⋮d\)
\(\Leftrightarrow14m+62⋮d\)
\(\Leftrightarrow\left(14m+63\right)-\left(14m+62\right)⋮d\)
\(14m+63-14m-62⋮d\)
\(1⋮d\)
\(\Leftrightarrow\dfrac{2m+9}{14m+62}\)tối giản với mọi m
