To get the common denominator you would multiply the first term by (x-4)/(x-4) and you multiply the second term by (x+4)/(x+4):
(x-4) 4 + x (x+4)
(x-4)(x+4). (x-4)(x+4)
The next step is to distribute the 4 (x-4) and the x (x+4)
so now you have
4x-16 + x^2 + 4x
(x - 4) (x + 4)
now combine like terms and put them in order exponents
x^2 + 8x - 16
(x-4)(x+4)
Since x^2 + 8x - 16 is not factorable you are done. That is your answer:
x^2 + 8x - 16
(x-4)(x+4)
