This expression can be simplified by factoring out the common denominator of (1-b)(1+b) on the right side:

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

Now, we can rewrite the last term as a sum of simpler fractions:

a/(1-b) + a/(1+b) + a/((1-b)(1+b))

Next, we can combine the first two fractions by finding a common denominator of (1-b)(1+b):

[a(1+b) + a(1-b)] / ((1-b)(1+b))

Now, simplifying the numerator gives:

[a + ab + a - ab] / ((1-b)(1+b))

Which simplifies further to:

[2a] / [1-b^2]

Therefore, the simplified expression is:

2a / (1 - b^2)