Question

1. divide: $dfrac{x^{2} + 10x + 16}{x^{2} - 6x - 16} div dfrac{x + 8}{x^{2} - 64}$

options:
$x - 8$
$dfrac{x + 2}{x + 8}$
$x + 8$
$dfrac{x + 8}{x + 2}$

Explanation:

Step1: Factor numerators/denominators

$x^2+10x+16=(x+2)(x+8)$, $x^2-6x-16=(x-8)(x+2)$, $x^2-64=(x-8)(x+8)$

Step2: Rewrite division as multiplication

$\frac{(x+2)(x+8)}{(x-8)(x+2)} \times \frac{(x-8)(x+8)}{x+8}$

Step3: Cancel common factors

Cancel $(x+2)$, $(x+8)$, $(x-8)$ → $x+2$

Answer:

(Assuming the first option is $x-8$, but based on calculation, the correct simplified form is $(x+2)(x-8)/(x-8) = x+2$, but since options are unclear, if one option is $x+2$, that's the answer. However, from visible options, if none match, but likely the intended answer is $x+2$)