To simplify this expression, we need to first find a common denominator for all the fractions involved.

Given expression: (4a/(a^2-1) + (a-1)/(a+1)) * (2a/(a+1) - a/(a-1) - a/(a^2-1))

First, factor the denominators where possible:
a^2 - 1 = (a+1)(a-1)
a^2 - 1 = (a+1)(a-1)
a^2 - 1 = (a+1)(a-1)

Next, rewrite the expression with the factored denominators:
(4a/((a+1)(a-1)) + (a-1)/(a+1)) * (2a/(a+1) - a/(a-1) - a/((a+1)(a-1)))

Now, find a common denominator for all fractions in the expression:
Common denominator = (a+1)(a-1)

Rewrite the expression with the common denominator:
(4a(a+1)/((a+1)(a-1)) + (a-1)^2/((a+1)(a-1))) * (2a(a-1)/((a+1)(a-1)) - a(a+1)/((a+1)(a-1)) - a/((a+1)(a-1)))

Now, simplify each fraction:
= (4a^2 + 4a + a^2 - 2a + 1)/((a+1)(a-1)) (2a^2 - 2a - a^2 - a - a^2 + a)/((a+1)(a-1))
= (5a^2 + 2a + 1)/((a+1)(a-1)) (0)/((a+1)(a-1))
= 0

Therefore, the simplified expression is 0.