Question

which expression is equal to \\(\frac{x + 2}{x + 8} \div \frac{x^2 + 14}{(x + 8)(x - 5)}\\)?\\(\bigcirc\\) \\(\frac{(x + 2)(x^2 + 14)}{(x + 8)(x - 5)}\\)\\(\bigcirc\\) \\(\frac{(x + 2)}{x^2 + 14}\\)\\(\bigcirc\\) \\(\frac{(x + 2)(x^2 + 14)}{(x + 8)^3(x - 5)}\\)\\(\bigcirc\\) \\(\frac{(x + 2)(x - 5)}{x^2 + 14}\\)

Explanation:

Step1: Rewrite division as multiplication

$\frac{x+2}{x+8} \div \frac{x^2+14}{(x+8)(x-5)} = \frac{x+2}{x+8} \times \frac{(x+8)(x-5)}{x^2+14}$

Step2: Cancel common factors

Cancel $(x+8)$ from numerator and denominator:
$\frac{x+2}{\cancel{x+8}} \times \frac{\cancel{(x+8)}(x-5)}{x^2+14} = \frac{(x+2)(x-5)}{x^2+14}$

Answer:

$\boldsymbol{\frac{(x+2)(x-5)}{x^2+14}}$ (corresponding to the last option)