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