To simplify this expression, we need to find common denominators for the fractions.

First, let's factor the denominators:
b^2+3 = (b+√3)(b-√3)
b^4-9 = (b^2+3)(b^2-3) = (b+√3)(b-√3)(b+√3)(b-√3) = (b+√3)^2(b-√3)^2

Now, the common denominator will be the product of these factors: (b+√3)(b-√3)(b+√3)^2(b-√3)^2.

Now, let's rewrite the fractions with the common denominator:

2/(3+b^2) = 2/((b+√3)(b-√3)) = (2(b+√3)(b-√3))/((b+√3)(b-√3)(b+√3)(b-√3)) = 2(b+√3)(b-√3)/(b+√3)^2(b-√3)^2

12/(b^4-9) = 12/((b+√3)^2(b-√3)^2)

2/(3-b^2) = 2/((b-√3)(b+√3)) = (2(b-√3)(b+√3))/((b-√3)(b+√3)(b+√3)(b-√3)) = 2(b-√3)(b+√3)/(b+√3)^2(b-√3)^2

Putting it all together, we have:

2(b+√3)(b-√3)/(b+√3)^2(b-√3)^2 - 12/((b+√3)^2(b-√3)^2) - 2(b-√3)(b+√3)/(b+√3)^2(b-√3)^2

Now, simplify as needed.