Ta có:2x=2x-2.2+2.2=2.(x-2)+4.Vì 2.(x-2)\(⋮\)x-2 nên 4 sẽ chia hết cho x-2\(\Rightarrow\)x-2\(\in\)Ư(4)={\(\pm\)1,\(\pm\)2,\(\pm\)4}.Ta có:x-2=-1;x-2=1;x-2=-2;x-2=2;x-2=-4;x-2=4.Lần lượt ta có x\(\in\){1,3,0,4,-2,6}
+ \(2x⋮x-2\)
\(\Leftrightarrow2\left(x-2\right)+4⋮x-2\)
\(\Leftrightarrow4⋮x-2\)
\(\Leftrightarrow x-2\in\left\{-4;-2;-1;1;2;4\right\}\)
\(\Leftrightarrow x\in\left\{-2;0;1;3;4;6\right\}\)