I presume this is

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

Please use parenthesis!

Like adding any other kind of fraction, you need a common denominator. So factor

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

The first fraction only has a b - 1 in its denominator, so we need to multiply top and bottom by b + 1:

b/(b - 1) * (b + 1)/(b + 1) + 2b/[(b + 1)(b - 1)]

= b(b + 1)/[(b + 1)(b - 1)] + 2b/[(b + 1)(b - 1)]

= [b(b + 1) + 2b]/[(b + 1)(b - 1)]

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

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

= [b(b + 3)]/[(b + 1)(b - 1)]

-Dan