e, ĐK: \(x\ne2\)
\(\dfrac{3}{x-2}>1\Leftrightarrow\dfrac{5-x}{x-2}>0\)
\(\Leftrightarrow\left\{{}\begin{matrix}5-x>0\\x-2>0\end{matrix}\right.\left(1\right)\) hoặc \(\left\{{}\begin{matrix}5-x< 0\\x-2< 0\end{matrix}\right.\left(2\right)\)
\(\left(1\right)\Leftrightarrow2< x< 5\)
\(\left(2\right)\Leftrightarrow\) vô nghiệm
Vậy \(2< x< 5\)
f, ĐK: \(x\ne\dfrac{1}{2}\)
\(\dfrac{2x^2+x}{1-2x}\ge1-x\)
\(\Leftrightarrow\dfrac{2x^2+x+\left(x-1\right)\left(1-2x\right)}{\left(1-2x\right)\left(x-1\right)}\ge0\)
\(\Leftrightarrow\dfrac{4x-1}{\left(1-2x\right)\left(x-1\right)}\ge0\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x-1\ge0\\\left(1-2x\right)\left(x-1\right)>0\end{matrix}\right.\left(1\right)\) hoặc \(\left\{{}\begin{matrix}4x-1\le0\\\left(1-2x\right)\left(x-1\right)< 0\end{matrix}\right.\left(2\right)\)
\(\left(1\right)\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{4}\\\dfrac{1}{2}< x< 1\end{matrix}\right.\Leftrightarrow\dfrac{1}{2}< x< 1\)
\(\left(2\right)\Leftrightarrow\left\{{}\begin{matrix}x\le\dfrac{1}{4}\\\left[{}\begin{matrix}x>1\\x< \dfrac{1}{2}\end{matrix}\right.\end{matrix}\right.\Leftrightarrow x\le\dfrac{1}{4}\)
Vậy ...
