Question

Giải: \(\dfrac{x+2}{x-3}< 0\).

Answer 1

\(\dfrac{x+2}{x-3}< 0\) (ĐK: x khác 3)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2< 0\\x-3>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+2>0\\x-3< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< -2\\x>3\end{matrix}\right.\\\left\{{}\begin{matrix}x>-2\\x< 3\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-2>x>3\left(vô-lý\right)\\-2< x< 3\end{matrix}\right.\)

Vậy: -2 < x < 3 (t/m đk)

Answer 2