The expression can be simplified as:
a^2 - b^2 + (a / (a^2 + b^2)) + (b / (a^2 + b^2 - b)) - (a / (a - (a^2 + b^2)))
Using the identity a^2 - b^2 = (a + b)(a - b), the expression becomes:
(a + b)(a - b) + (a / (a^2 + b^2)) + (b / (a^2 + b^2 - b)) - (a / (a - (a^2 + b^2)))
And since a/a = 1, the expression can be further simplified as:
(a + b)(a - b) + 1 + (b / (a^2 + b^2 - b)) - (a / (a - (a^2 + b^2)))
This is the simplified form of the expression