Gọi ƯCLN\(\left(2n+3;3n+7\right)=d\)
\(\Rightarrow\orbr{\begin{cases}2n+3⋮d\Rightarrow3.\left(2n+3\right)⋮d\Rightarrow6n+9⋮d\\3n+7⋮d\Rightarrow2.\left(3n+7\right)⋮d\Rightarrow6n+14⋮d̸\end{cases}}\)
\(\Rightarrow\left(6n+14\right)-\left(6n+9\right)⋮d\)
\(\Rightarrow5⋮d\Rightarrow d\in1;5\)
\(+d=5\Rightarrow6n+9⋮5\Rightarrow5n+\left(n+9\right)⋮5\)
\(\Rightarrow n+9⋮5\Rightarrow n+4⋮5\Rightarrow n=5k-4\)
Vậy n=5k-4 thì rút gọn đc
Vậy \(n\ne5k-4\Rightarrowđpcm\)
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