$\begin{array}{l}
f\left( x \right) = \sqrt {4x + 1} - \sqrt { - 2x + 1} \\
DK:\left\{ \begin{array}{l}
4x + 1 \ge 0\\
- 2x + 1 \ge 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ge - \frac{1}{4}\\
x \le \frac{1}{2}
\end{array} \right. \Leftrightarrow - \frac{1}{4} \le x \le \frac{1}{2}\\
\Rightarrow TXD:D = \left[ { - \frac{1}{4};\frac{1}{2}} \right]\\
f\left( x \right) = \frac{{2x + 1}}{{\left( {2x + 1} \right)\left( {x - 3} \right)}}\\
DK:\left\{ \begin{array}{l}
2x + 1 \ne 0\\
x - 3 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne - \frac{1}{2}\\
x \ne 3
\end{array} \right.\\
\Rightarrow TXD:D = R\backslash \left\{ { - \frac{1}{2};3} \right\}
\end{array}$
