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: Rewrite division as multiplication

$\frac{x^2 + 10x + 16}{x^2 - 6x - 16} \times \frac{x^2 - 64}{x + 8}$

Step2: Factor numerators and denominators

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

Step3: Cancel common factors

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

Answer:

$x - 8$