Để \(A>1\Rightarrow-\dfrac{5}{x+6}>1\)
\(\Leftrightarrow-\dfrac{5}{x+6}-1>0\)
\(\Leftrightarrow\dfrac{-5-x-6}{x+6}>0\)
\(\Leftrightarrow\dfrac{-x-11}{x+6}>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}-x-11>0\\x+6>0\end{matrix}\right.\\\left\{{}\begin{matrix}-x-11< 0\\x+6< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-11\\x>-6\end{matrix}\right.\\\left\{{}\begin{matrix}x< -11\\x< -6\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>-6\\x< -11\end{matrix}\right.\)
Vậy x>-6 hoặc x<-11 thì A>1
\(\dfrac{-5}{x+6}\) >1 <=> -5 > x+6 <=> -5 -6 > x <=> -11 > x
hay x< -11 thì A>1
\(A=\dfrac{-5}{x+6},A>1\)
\(\Rightarrow\dfrac{-5}{x+6}>1\) (ĐK: \(x\ne-6\))
\(\Leftrightarrow\dfrac{-5}{x+6}-1>0\)
\(\Leftrightarrow\dfrac{-5-x-6}{x+6}>0\)
\(\Leftrightarrow\dfrac{-x-11}{x+6}>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}-x-11>0\Leftrightarrow x< -11\\x+6>0\Leftrightarrow x>-6\end{matrix}\right.\\\left\{{}\begin{matrix}-x-11< 0\Leftrightarrow x>-11\\x+6< 0\Leftrightarrow x< -6\end{matrix}\right.\end{matrix}\right.\)(x không thể < -11 và > -6)
\(\Leftrightarrow-11< x< -6\)
Với A > 1 khi -11 < x < -6
