Question

I need to solve for x

Answer 1

Looks like a whole lot of fun you got there... Okay.. so first you'd have to add up the two values on the left side by multiplying the top and bottom of the first by the denominator of the second and by multiplying the top and bottom of the second by the denominator of the first, like this (sorry for all the parentheses) :
[x(x-4)]/[(x+4)(x-4)] + [4(x+4)]/[(x+4)(x-4)]. now you can add them together:
[x(x-4)+4(x+4)]/[(x+4)(x-4)] then i'd try to combine the top: 
x^2-4x+4x+16 or x^2+16, then i'd combine the bottom (since i just noticed something awesome here):
x^2-4x+4x-16 or x^2-16. This makes the left side look exactly like the right ( isn't that awesome!) This means x = 1!