a) Ta có:6 chia hết cho(x-1)
\(\Rightarrow x-1\inƯ\left(6\right)=\left\{1;2;3;6\right\}\)
+Nếu x-1=1 \(\Rightarrow\)x=1+1=2
+Nếu x-1=2 \(\Rightarrow\)x=2+1=3
+ Nếu x-1=3 \(\Rightarrow\)x=3+1=4
+Nếu x-1=6 \(\Rightarrow\)x=6+1=7
Vậy \(x\in\left\{2;3;4;7\right\}\)
b)Ta có:14 chia hết cho (2x+3)
\(\Rightarrow\left(2x+3\right)\inƯ\left(14\right)=\left\{1;2;4;7;14\right\}\)
Vì \(x\in N\),nên \(2x+3\ge3\)và 2x+3 là số lẻ
\(\Rightarrow2x+3=7\)
\(2x=7-3=4\)
\(x=\frac{4}{2}\)
\(x=2\)
Vậy x=2