Đáp án:
$\begin{array}{l}
1)\left\{ \begin{array}{l}
x \ne 0\\
x + 1 \ne 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x \ne 0\\
x \ne - 1
\end{array} \right.\\
2)x + 1 \ne 0 \Rightarrow x \ne - 1\\
3)\left\{ \begin{array}{l}
x - 2 > 0\\
x - 3 \ne 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x > 2\\
x \ne 3
\end{array} \right.\\
4)\\
\left\{ \begin{array}{l}
x - 3 \ge 0\\
\left| x \right| \ne \sqrt {x - 3} \\
16 - 2x \ge 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x \ge 3\\
{x^2} \ne x - 3\\
x \le 8
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
3 \le x \le 8\\
{x^2} - x + 3 \ne 0\left( {ld} \right)
\end{array} \right.\\
\Rightarrow 3 \le x \le 8
\end{array}$