Derivative of Natural Log

Can someone please tell me what I'm doing wrong here, and show me how to do it correctly?

I need to differentiate g(x) = LN a-x/a+x

So,

g'(x) = 1/a-x/a+x *d/dx (a-x/a+x)

g'(x) = a+x/a-x *[(a+x)*d/dx(a-x) - (a-x)*d/dx(a+x)/(a+x)^2]

g'(x) = a+x/a-x *[(a+x)*(1-1) - (a-x)(1+1)/(a+x)^2]

g'(x) = a+x/a-x *[(a+x)*(0) - (a-x)(2)/(a+x)^2]

g'(x) = a+x/a-x *[0 - 2(a-x)/(a+x)^2]

g'(x) = a+x/a-x * -2a+2x/a^2+2ax+x^2

g'(x) = a+x*(-2a+2x)/a-x*(a^2+2ax+x^2)

g'(x) = -2a^2+2ax-2ax+2x^2/a^3+2a^2x+ax^2-a^2x-2ax^2-x^3)

g'(x) = -2a^2+2x^2/(a^3+a^2x-ax^2-x^3)

the answer is supposed to be g'(x) = -2a/a^2-x^2, but that's not what I get when I simplify . . .