Question

Perform each indicated operation

Answer 1

Answer: $\frac{x+6}{x-4}$

Step-by-step explanation:

First you need know some general formuals of factorization such as

$x^3+y^3=(x+y)(x^2-xy+y^2)$ so you have $x^3+64=X^3+4^3=(x+4)(x^2-4x+4^2)$

And, $x^2-y^2=(x-y)(x+y)$ so you have $2x^2-32=2(x^2-16)=2(x^2-4^2)=2(x+4)(x-4)$

If you use them, then you can modify your equations such as

$\frac{x^3+64}{2x^2-32}$ ÷ $\frac{x^2-4x+16}{2x+12}$ = $\frac{(x+4)(x^2-4x+4^2)}{2(x+4)(x-4)}$ ÷ $\frac{x^2-4x+16}{2(x+6)}$  =  $\frac{(x+4)(x^2-4x+4^2)}{2(x+4)(x-4)} . \frac{2(x+6)}{{x^2-4x+16}} = \frac{1}{x-4}.\frac{x+6}{1}=\frac{x+6}{x-4}$