1. The inequality is equivalent to

$$
\begin{gathered}
\frac{\sqrt{x^{2}+14 x+40}-2 \sqrt{x^{2}-x-2}}{\left(\sqrt{x^{2}-x-2}-2\right)\left(\sqrt{x^{2}+14 x+40}-4\right)} \leqslant 0 \Leftrightarrow \\
\left\{\begin{array} { l } 
{ \frac { x ^ { 2 } + 1 4 x + 4 0 - 4 ( x ^ { 2 } - x - 2 ) } { ( x ^ { 2 } - x - 6 ) ( x ^ { 2 } + 1 4 x + 2 4 ) } \leqslant 0 , } \\
{ x ^ { 2 } - x - 2 \geqslant 0 , } \\
{ x ^ { 2 } + 1 4 x + 4 0 \geqslant 0 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
\frac{(x-8)(x+2)}{(x-3)(x+2)^{2}(x+12)} \geqslant 0 \\
(x+1)(x-2) \geqslant 0 \\
(x+10)(x+4) \geqslant 0
\end{array}\right.\right.
\end{gathered}
$$
Answer: $(-\infty ;-12) \cup(-2 ;-1] \cup[2 ; 3) \cup[8 ;+\infty)$.

Answer to option $6-2: (-\infty ;-13) \cup(-3 ;-2] \cup[1 ; 2) \cup[7 ;+\infty)$.