(4/x+4)+(x/x-4) find the comoon denominator and then add. show your work

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

x^2 + 8x - 16
(x-4)(x+4)