\[\frac{x^{4} - 10x^{2} + 9}{4x + 12} \leq 0\]
\[x^{4} - 10x^{2} + 9 =\]
\[= (x + 3)(x + 1)(x - 1)(x - 3)\]
\[Пусть\ x^{2} = y:\]
\[y^{2} - 10y + 9 = 0\]
\[D_{1} = 25 - 9 = 16\]
\[y_{1} = 5 + 4 = 9;\ \ y_{2} = 5 - 4 = 1.\]
\[1)\ x^{2} = 9\]
\[x = \pm 3.\]
\[2)\ x^{2} = 1\]
\[x = \pm 1.\ \]
\[\frac{(x + 3)(x + 1)(x - 1)(x - 3)}{4 \cdot (x + 3)} \leq 0\]
\[x < - 3;\ - 3 < x \leq - 1;\ \ \]
\[1 \leq x \leq 3.\]