Để biểu thức \(\sqrt{\frac{2x-1}{x+3}}\) được xác định thì
\(\left\{{}\begin{matrix}\frac{2x-1}{x+3}\ge0\\x+3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1\ge0\\x+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1\le0\\x+3< 0\end{matrix}\right.\end{matrix}\right.\\x\ne-3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\frac{1}{2}\\x>-3\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\frac{1}{2}\\x< -3\end{matrix}\right.\end{matrix}\right.\\x\ne-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge\frac{1}{2}\\x< -3\end{matrix}\right.\\x\ne-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x\ge\frac{1}{2}\\x< -3\end{matrix}\right.\)
