a/ \(n+9⋮n+4\)

Mà \(n+4⋮n+4\)

\(\Leftrightarrow5⋮n+4\)

Vì \(n\in N\Leftrightarrow n+4\in N;n+4\inƯ\left(5\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}n+4=1\+4=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=-3\left(loại\right)\=1\left(tm\right)\end{matrix}\right.\)

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b/ \(3n+40⋮n+4\)

Mà \(n+4⋮n+4\)

\(\Leftrightarrow\left\{{}\begin{matrix}3n+40⋮n+4\\3n+12⋮n+4\end{matrix}\right.\)

\(\Leftrightarrow28⋮n+4\)

Vì \(n\in N\Leftrightarrow n+4\in N;n+4\inƯ\left(28\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}n+4=1\+4=28\+4=2\+4=14\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=-3\left(loại\right)\=24\=-2\left(loại\right)\=10\end{matrix}\right.\)

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c/ \(5n+2⋮2n+9\)

Mà \(2n+9⋮2n+9\)

\(\Leftrightarrow\left\{{}\begin{matrix}10n+4⋮2n+9\\10n+45⋮2n+9\end{matrix}\right.\)

\(\Leftrightarrow41⋮2n+9\)

\(\Leftrightarrow2n+9\inƯ\left(41\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}2n+9=1\\2n+9=41\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}n=-4\left(loại\right)\=16\end{matrix}\right.\)

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