Question

Answer 1

a, \(-x^2+6x-5< x^2+x-30\Leftrightarrow2x^2-5x-25>0\)

\(\Leftrightarrow\left(2x+5\right)\left(x-5\right)>0\Leftrightarrow x< -\dfrac{5}{2};x>5\)

b, \(\dfrac{3\left(x-5\right)}{1-x}-2\le0\Leftrightarrow\dfrac{3x-15-2+2x}{1-x}\le0\Leftrightarrow\dfrac{5x-17}{1-x}\le0\)

TH1 : \(\left\{{}\begin{matrix}5x-17\le0\\1-x>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le\dfrac{17}{5}\\x< 1\end{matrix}\right.\Leftrightarrow x< 1\)

TH2 : \(\left\{{}\begin{matrix}5x-17\ge0\\1-x< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{17}{5}\\x>1\end{matrix}\right.\Leftrightarrow x\ge\dfrac{17}{5}\)