Đáp án:
1) $ {\left\{\begin{aligned}n \neq -2\\n\neq 5\\ n \neq 3\end{aligned}\right.}$
2)
$a) n=\{...,-10,-2,6,14,22,30,...\}\\
b) n=\{3,-3,-4,-10\}\\
c) n=\{-1,0\}$
Giải thích các bước giải:
1) điều kiện ${\left\{\begin{aligned}2n+4 \neq 0\\n-5\neq 0\\ 3n-9 \neq 0\end{aligned}\right.}$
$\Rightarrow {\left\{\begin{aligned}2n \neq -4\\n\neq 5\\ 3n \neq 9\end{aligned}\right.}\\
\Leftrightarrow {\left\{\begin{aligned}n \neq -2\\n\neq 5\\ n \neq 3\end{aligned}\right.}$
2)
$a) \frac{n+2}{8}\\
\Rightarrow n+2 \in B(8)=\{,...,-8,0,8,16,24,32,....\}\\
\Rightarrow n=\{...,-10,-2,6,14,22,30,...\}\\
b) \frac{2n+20}{2n+7}\\
\Rightarrow 2n+20 \vdots 2n+7\\
\Leftrightarrow 2n+7 +13 \vdots 2n+7\\
\Leftrightarrow 13\vdots 2n+7\\
\Leftrightarrow 2n+7 \in U(13)=\{13,1,-1,-13\}\\
+) 2n+7=13\Rightarrow 2n=13-7=6\Rightarrow n=3\\
+) 2n+7=1\Rightarrow 2n=1-7=-6\Rightarrow n=-3\\
+) 2n+7=-1\Rightarrow 2n=-1-7=-8\Rightarrow n=-4\\
+) 2n+7=-13\Rightarrow 2n=-13-7=-20\Rightarrow n=-10\\
\Rightarrow n=\{3,-3,-4,-10\}\\
c) \frac{8n-1}{4n+1}\\
\Rightarrow 8n-1 \vdots 4n+1\\
\Rightarrow 2(4n+1)-3 \vdots 4n+1\\
\Rightarrow -3\vdots 4n+1\\
\Rightarrow 4n+1 \in U(3)=\{-1,-3,1,3\}\\
+) 4n+1=-1\Rightarrow 4n=-1-1=-2\Rightarrow n=\frac{-1}{2}\\
+) 4n+1=-3\Rightarrow 4n=-3-1=-4\Rightarrow n=-1\\
+) 4n+1=1\Rightarrow 4n=1-1=0\Rightarrow n=0\\
+) 4n+1=3\Rightarrow 4n=3-1=2\Rightarrow n=\frac{1}{2}\\
\Rightarrow n=\{-1,0\}$
