Question

Tìm các giá trị của x để biểu thức có nghĩa: d) \(\sqrt{\dfrac{x+3}{5-x}}\)

Answer 1

\(\sqrt{\dfrac{x+3}{5-x}}\) xác định \(\Leftrightarrow\dfrac{x+3}{5-x}\ge0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+3\ge0\\5-x>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+3\le0\\5-x< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge-3\\x< 5\end{matrix}\right.\\\left\{{}\begin{matrix}x\le-3\\x>5\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow-3\le x< 5\)

Answer 2

để:\(\sqrt{\dfrac{x+3}{5-x}}\) thì: \(\dfrac{x+3}{5-x}\ge0\) (x≠5)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+3\le0\\5-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+3\ge0\\5-x>0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le-3\\x>5\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge-3\\x< 5\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow-3\le x< 5\)

vậy............