Answer:
A. 4(x - 6)/(x + 6)
Explanation:
The given expression is
[tex]\frac{x^2-36}{x+8}\div\frac{x^2+12x+36}{4x+32}[/tex]
To divide by a fraction is equivalent to multiplying by the reciprocal of the fraction, so this expression is equivalent to
[tex]\frac{x^2-36}{x+8}\times\frac{4x+32}{x^2+12x+36}=\frac{(x^2-36)(4x+32)}{(x+8)(x^2+12x+36)}[/tex]
Now, we need to factorize the following expressions as
(x² - 36) = (x + 6)(x - 6)
4x + 32 = 4(x + 8)
x² + 12x + 36 = (x + 6)²
So, the expression is equal to
[tex]\frac{(x+6)(x-6)4(x+8)}{(x+8)(x+6)^2}=\frac{4(x-6)}{(x+6)}[/tex]
Therefore, the answer is
A. 4(x - 6)/(x + 6)
