`a)`

`A = \frac{n+3}{-n-4}`.

Để `A \in \mathbb{Z}` thì `(n+3) \vdots (n+4)`

`⇒ (n+4-1) \vdots (n+4)`

`⇒ 1 \vdots (n+4)` 

`⇔ n+4 \in \{1; -1\}`

`→ n \in \{-3; -5\}`

Vậy `n \in \{-3; -5\}`

`---`

`b)`

`B = \frac{-6}{n+5}`

Để `B \in \mathbb{Z}` thì `-6 \vdots (n+5)`

`⇒ n+5 \in Ư(-6) = \{1; -1; 2; -2; 3; -3; 6; -6\}`

Ta có bảng giá trị:

\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline n+5 & 1 & -1 & 2 & -2 & 3 & -3 & 6 & -6 \\\hline n & -4 & -6 & -3 & -7 & -2 & -8 & 1 & -11 \\\hline\end{array}

Vậy `n \in \{1; -2; -3; -4; -6; -7; -8; -11\}`