\(\dfrac{x^2-2x-4}{x^2-2x-3}>1\)
\(\Leftrightarrow\dfrac{x^2-2x-4}{x^2-2x-3}-1>0\)
\(\Leftrightarrow\dfrac{x^2-2x-4-x^2+2x+3}{x^2-3x+x-3}>0\)
\(\Leftrightarrow\dfrac{-1}{\left(x-3\right)\left(x+1\right)}>0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3>0\\x+1< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-3< 0\\x+1>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>3\\x< -1\end{matrix}\right.\\\left\{{}\begin{matrix}x< 3\\x>-1\end{matrix}\right.\end{matrix}\right.\)
TH1 : vô lý
Vậy \(-1< x< 3\) thì \(\dfrac{x^2-2x-4}{x^2-2x-3}>1\)
\(\dfrac{x^2-2x-4}{x^2-2x-3}>1\)
\(\Leftrightarrow x^2-2x-4>x^2-2x-3\)
\(\Leftrightarrow x^2-x^2-2x+2x>-3+4\)
\(\Leftrightarrow0x>1\) (vô lí)
Vậy bpt vô nghiệm
