Question

What is the quotient of the rational expression below? *photo

Answer 1

A. 4(x - 6)/(x + 6)

Step-by-step explanation:

The given expression is

`(x^2-36)/(x+8)/(x^2+12x+36)/(4x+32)`

To divide by a fraction is equivalent to multiplying by the reciprocal of the fraction, so this expression is equivalent to

`(x^2-36)/(x+8)*(4x+32)/(x^2+12x+36)=((x^2-36)(4x+32))/((x+8)(x^2+12x+36))`

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

`((x+6)(x-6)4(x+8))/((x+8)(x+6)^2)=(4(x-6))/((x+6))`

Therefore, the answer is

A. 4(x - 6)/(x + 6)