Did I write the correct equivalent

Is a+2 equivalent to

2a³-16
_________
2a²+4a+8

or
2a^3-16/2a^2+4a+8?

2a³-16
_________
2a²+4a+8

= a³-8
_________
a²+2a+4

= (a-2)(a²+2a+4)
_________________
a²+2a+4

= a-2

2a³-16
_________
2a²+4a+8

a³ - 8
_________
a² + 2a + 4

x^3− y^3 = (x − y)(x2 + xy + y2) ...difference of cubes...note that 8 = 2^3

(a - 2)*(a^2 + 2*a +4)/(a^2 + 2*a + 4)

= a - 2 <<<

Not sure that helps...

Top line is 2a³-16 = 2(a-2)(a^2+2a+4)

Bottom line is 2a^2+4a+8) = 2(a^2+2a+4)

So answer is (a-2)

(2a^3 - 16) / (2a^2 + 4a + 8) = a - 2