a) Ta có:
\(6⋮2x-1\)
\(\Rightarrow2x-1\in U\left(6\right)=\left\{1;2;3;6\right\}\) \(\left(\text{ vì }x\in N\right)\)
\(\Rightarrow\left\{{}\begin{matrix}2x-1=1\Rightarrow x=1\\2x-1=2\Rightarrow x=1,5\left(loai\right)\\2x-1=3\Rightarrow x=2\\2x-1=6\Rightarrow3,5\left(loai\right)\end{matrix}\right.\)
Vậy x=1 hoặc x=2
b) Ta có:
\(x+5⋮x-1\)
\(\Rightarrow\left(x-1\right)+6⋮x-1\)
\(\Rightarrow6⋮x-1\)
\(\Rightarrow x-1\in U\left(6\right)=\left\{1;2;3;6\right\}\) \(\left(\text{ vì }x\in N\right)\)
\(\Rightarrow\left\{{}\begin{matrix}x-1=1\Rightarrow x=2\\x-1=2\Rightarrow x=3\\x-1=3\Rightarrow x=4\\x-1=6\Rightarrow x=7\end{matrix}\right.\)
Vậy x=2 hoặc x=3 hoặc x=4 hoặc x=7
