\(\text{b) Để }\frac{x-25}{x+4}\inℤ\text{ thì }x-25⋮x+4\)
\(\Leftrightarrow x+4-29⋮x+4\)
\(\text{Vì }x+4⋮x+4\Leftrightarrow29⋮x+4\)
\(\Leftrightarrow x+4\inƯ\left(29\right)\)
\(\Leftrightarrow x+4\in\left\{\pm1;\pm29\right\}\)
\(\Leftrightarrow\orbr{\begin{cases}x+4=\pm1\\x+4=\pm29\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-3;-5\\x=25;-33\end{cases}}\)
\(\Leftrightarrow x\in\left\{-3;-5;25;-33\right\}\)