$\{\begin{array}{c}\frac{4-\sqrt{x^2+7x+10}}{x}<-2\\ x^4-16x^2\le 0\end{array}$

• $\frac{4-\sqrt{x^2+7x+10}}{x}<-2\Rightarrow \frac{4-\sqrt{x^2+7x+10}+2x}{x}<0\Rightarrow \frac{\sqrt{x^2+7x+10}-2x-4}{x}>0$
  • $\sqrt{x^2+7x+10}>2x+4\Rightarrow \{\begin{array}{c}2x+4\ge 0\\ x^2+7x+10>{\left(2x+4\right)}^2\end{array}\vee \{\begin{array}{c}2x+4<0\\ x^2+7x+10\ge 0\end{array}\Rightarrow \{\begin{array}{c}x\ge -2\\ x^2+3x+2<0\end{array}\vee \{\begin{array}{c}x<-2\\ x\le -5\vee x\ge -2\end{array}\Rightarrow$

    $\Rightarrow \{\begin{array}{c}x\ge -2\\ -2<x<-1\end{array}\vee x\le -5\Rightarrow$$x\le -5\vee -2<x<-1$

  • $x>0$

  $-1<x<0$

  
  
• $x^4-16x^2\le 0\Rightarrow x^2(x^2-16)\le 0\Rightarrow$$-4\le x\le 4$

$-1<x<0$