\[\frac{x^{2} + 12x + 37}{x^{2} + 11} \geq 0\]
\[x^{2} + 12x + 37 \geq 0\]
\[x^{2} + 12x + 36 + 1 \geq 0\]
\[\left( x^{2} + 6 \right) + 1 \geq 0 - верно\ \]
\[для\ любого\ x \in R.\]
\[Ответ:( - \infty; + \infty).\]