To simplify the expression, let's first find a common denominator for both fractions:

(2b^2 - b) / (b^3 + 1) - (b - 1) / (b^2 + 1 - b)

To simplify the expression further, we need to factor the denominator in the first fraction:

b^3 + 1 = (b + 1)(b^2 - b + 1)

Now, rewrite the expression with common denominators:

(2b^2 - b)(b + 1) / (b + 1)(b^2 - b + 1) - (b - 1) / (b^2 + 1 - b)

Now, let's simplify the fractions:

[(2b^3 + 2b^2 - b^2 - b) - (b^2 - b + 1)] / (b^2 - b + 1)

Simplify the numerator:

(2b^3 + b^2 - b - 1 - b^2 + b - 1) / (b^2 - b + 1)
(2b^3 - 2) / (b^2 - b + 1)

Therefore, the simplified expression is:
(2b^3 - 2) / (b^2 - b + 1)