1) \(A=\dfrac{4}{2x+1}\in Z\)
\(\Rightarrow2x+1\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
Do \(x\in Z\)
\(\Rightarrow x\in\left\{-1;0\right\}\)
2) \(B=\dfrac{x+1}{x-2}=1+\dfrac{3}{x-2}\in Z\)
\(\Rightarrow x-2\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\)
\(\Rightarrow x\in\left\{-1;1;3;5\right\}\)
3) \(C=\dfrac{2x-1}{x-3}=2+\dfrac{5}{x-3}\in Z\)
\(\Rightarrow x-3\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)
\(\Rightarrow x\in\left\{-2;2;4;8\right\}\)
4) \(D=\dfrac{6x+7}{2x+3}=\dfrac{3\left(2x+3\right)}{2x+3}-\dfrac{2}{2x+3}=3-\dfrac{2}{2x+3}\in Z\)
\(\Rightarrow2x+3\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\)
Do \(x\in Z\)
\(\Rightarrow x\in\left\{-2;-1\right\}\)
