Đáp án: C
Giải thích các bước giải:
$\begin{array}{l}
\frac{{ - 2{x^2} + 7x + 7}}{{{x^2} - 3x - 10}} \le - 1\\
\Leftrightarrow \frac{{ - 2{x^2} + 7x + 7 + {x^2} - 3x - 10}}{{{x^2} - 3x - 10}} \le 0\\
\Leftrightarrow \frac{{ - {x^2} + 4x - 3}}{{\left( {x - 5} \right)\left( {x + 2} \right)}} \le 0\\
\Leftrightarrow \frac{{{x^2} - 4x + 3}}{{\left( {x - 5} \right)\left( {x + 2} \right)}} \ge 0\\
\Leftrightarrow \frac{{\left( {x - 1} \right)\left( {x - 3} \right)}}{{\left( {x + 2} \right)\left( {x - 5} \right)}} \ge 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
\left( {x - 1} \right)\left( {x - 3} \right) \ge 0\\
\left( {x + 2} \right)\left( {x - 5} \right) > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
\left( {x - 1} \right)\left( {x - 3} \right) \le 0\\
\left( {x + 2} \right)\left( {x - 5} \right) < 0
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \ge 3/x \le 1\\
x > 5/x < - 2
\end{array} \right.\\
\left\{ \begin{array}{l}
1 \le x \le 3\\
- 2 < x < 5
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x > 5\\
x < - 2\\
1 \le x \le 3
\end{array} \right.\\
\Rightarrow R\backslash S = \left[ { - 2;1} \right) \cup \left( {3;5} \right]
\end{array}$
