Question

Perform each indicated operation

Answer 1

Answer:
`(x+6)/(x-4)`

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

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