simplify the rational trigonometric function. if the denominator is eliminated place a 1 in its answer box…

Explanation:

Step1: Factor the numerator

Let $t = \cos x$, then $\cos^{2}x-\cos x - 2=t^{2}-t - 2=(t - 2)(t+1)=(\cos x - 2)(\cos x + 1)$.

Step2: Factor the denominator

Factor out 6 from $6\cos x-12$, we get $6(\cos x - 2)$.

Step3: Simplify the function

$\frac{\cos^{2}x-\cos x - 2}{6\cos x-12}=\frac{(\cos x - 2)(\cos x + 1)}{6(\cos x - 2)}=\frac{\cos x + 1}{6}$.

Answer:

numerator = $\cos x+1$ denominator = $6$