1. ## very complicated algebra

Could someone help me with the following algebraic fraction:

$

\frac {(a-b)(a^2+b^2)-a+b}{(a^3b^3)-(a^2-ab+b^2)+1}
$

2. I think you have a typo somewhere because the denominator does not factor. The numerator factors to be
$(a-b)(a^2+b^2-1)$
So if there is no typo, then the rational function does not simplify any.