\(\text{a)}X=\frac{a-5}{a}\in Z\Rightarrow\frac{a}{a}-\frac{5}{a}\in Z\Rightarrow1-\frac{5}{a}\in Z\)
\(\Rightarrow\frac{5}{a}\in Z\Rightarrow a\in\text{Ư}\left\{5\right\}\)
\(\Rightarrow a\in\left\{-5;-1;1;5\right\}\)
\(\text{b)}X\in Z^+\Rightarrow\orbr{\begin{cases}a-5>0;a>0\\a-5< 0;a< 0\end{cases}\Rightarrow\orbr{\begin{cases}a>0\\a< 5\end{cases}}\Rightarrow\orbr{\begin{cases}a\in\left\{1;5\right\}\\a\in\varnothing\end{cases}}}\)
\(\Rightarrow a\in\left\{1;5\right\}\text{thì }X\in Z^+\)
\(\text{c)}X\in Z^-\Rightarrow\orbr{\begin{cases}a-5>0;a< 0\\a-5< 0;a>0\end{cases}\Rightarrow\orbr{\begin{cases}a>5;a< 0\\a< 5;a>0\end{cases}\Rightarrow}\orbr{\begin{cases}a\in\varnothing\\a\in\left\{1\right\}\end{cases}}}\)
\(\Rightarrow a=1\text{thì }X\in Z^-\)
