To simplify this expression, first, let's expand the numerator of the given expression:

(a + 1 + 1/a - 1)²
= (a + 1 + 1/a - 1)(a + 1 + 1/a - 1)
= a(a + 1 + 1/a) + 1(a + 1 + 1/a) - 1(a + 1 + 1/a) - 1
= a² + a + 1 + a + 1 + 1/a - a - 1 - 1/a - 1
= a² + 2 + 1/a

Now, simplify the denominator:
a^4/a^2 - 2a + 1
= a^2 - 2a + 1

Therefore, the simplified expression is:
(a² + 2 + 1/a) / (a² - 2a + 1)