a/ \(n+5⋮n-2\)

Mà \(n-2⋮n-2\)

\(\Leftrightarrow7⋮n-2\)

\(\Leftrightarrow n-2\inƯ\left(7\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}n-2=1\-2=7\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=3\=9\end{matrix}\right.\)

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b/ \(2n+3⋮n-3\)

Mà \(n-3⋮n-3\)

\(\Leftrightarrow\left\{{}\begin{matrix}2n+3⋮n-3\\2n-6⋮n-3\end{matrix}\right.\)

\(\Leftrightarrow9⋮n-3\)

\(\Leftrightarrow\left[{}\begin{matrix}n-3=1\-3=3\-3=9\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=4\=6\=12\end{matrix}\right.\)

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c/ \(2n+3⋮3n-2\)

Mà \(3n-2⋮3n-2\)

\(\Leftrightarrow\left\{{}\begin{matrix}6n+9⋮3n-2\\6n-4⋮3n-2\end{matrix}\right.\)

\(\Leftrightarrow13⋮3n-2\)

\(\Leftrightarrow3n-2\inƯ\left(13\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}3n-2=1\\3n-2=13\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=1\=5\end{matrix}\right.\)

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d/ \(n^2+2⋮n+1\)

Mà \(n+1⋮n+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}n^2+2⋮n+1\^2+1⋮n+1\end{matrix}\right.\)

\(\Leftrightarrow1⋮n+1\)

\(\Leftrightarrow n+1\inƯ\left(1\right)\)

\(\Leftrightarrow n+1=1\)

\(\Leftrightarrow n=0\)

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