Let's simplify the expression:

((a+b)^2)/(a^2+ab) + ((a-b)^2)/(ab-a^2)

= (a^2 + 2ab + b^2)/(a^2+ab) + (a^2 - 2ab + b^2)/(ab-a^2)

= (a^2 + 2ab + b^2)/(a(a+b)) + (a^2 - 2ab + b^2)/(-a(a-b))

= (a^2 + 2ab + b^2)/(a(a+b)) - (a^2 - 2ab + b^2)/(a(a-b))

= ((a+b)^2)/(a(a+b)) - ((a-b)^2)/(a(a-b))

= (a+b)/(a) - (a-b)/(a)

= 1 + 1

= 2

Therefore, the simplified expression is 2.