Answer
$$ - 6$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{x \to - \infty } \left( {\frac{9}{{{x^4}}} + \frac{{10}}{{{x^2}}} - 6} \right) \cr
& {\text{use the sum rule for limits }}\mathop {\lim }\limits_{x \to a} \left[ {f\left( x \right) \pm g\left( x \right)} \right] = \mathop {\lim }\limits_{x \to a} f\left( x \right) \pm \mathop {\lim }\limits_{x \to a} g\left( x \right) \cr
& = \mathop {\lim }\limits_{x \to - \infty } \frac{9}{{{x^4}}} + \mathop {\lim }\limits_{x \to - \infty } \frac{{10}}{{{x^2}}} - \mathop {\lim }\limits_{x \to - \infty } 6 \cr
& = 9\mathop {\lim }\limits_{x \to - \infty } \frac{1}{{{x^4}}} + 10\mathop {\lim }\limits_{x \to - \infty } \frac{1}{{{x^2}}} - \mathop {\lim }\limits_{x \to - \infty } 6 \cr
& {\text{evaluate the limits}}{\text{, use the rules }}\mathop {\lim }\limits_{x \to \infty } k = k{\text{ and }}\mathop {\lim }\limits_{x \to - \infty } \frac{1}{{{x^n}}} = 0 \cr
& = 9\left( 0 \right) + 10\left( 0 \right) - 6 \cr
& = - 6 \cr} $$
