To simplify this expression, we first expand the terms within the parentheses:
(a-1)^2 = a^2 - 2a + 1
Next, we simplify the expression (1/a^2 - 2a + 1 + 1/a^2 - 1):
1/a^2 + 1/a^2 = 2/a^2
-2a - 1 = -2a - 1
Therefore, the expression simplifies to:
(a^2 - 2a + 1)(2/a^2 - 2a - 1) + 2/a + 1
Expanding the terms:
((2a^2 - 4a + 2) / a^2 - (4a^3 - 8a^2 + 4a) - a^2 + 2a + 1
Now, simplify further:
((2a^2 - 4a + 2) / a^2 - 4a^3 + 8a^2 - 4a - a^2 + 2a + 1
Collecting like terms:
(2 + 2) / a^2 - 3a^2 + 6a + 1
4 / a^2 - 3a^2 + 6a + 1
Therefore, the simplified expression is:
4 / a^2 - 3a^2 + 6a + 1.
To simplify this expression, we first expand the terms within the parentheses:
(a-1)^2 = a^2 - 2a + 1
Next, we simplify the expression (1/a^2 - 2a + 1 + 1/a^2 - 1):
1/a^2 + 1/a^2 = 2/a^2
-2a - 1 = -2a - 1
Therefore, the expression simplifies to:
(a^2 - 2a + 1)(2/a^2 - 2a - 1) + 2/a + 1
Expanding the terms:
((2a^2 - 4a + 2) / a^2 - (4a^3 - 8a^2 + 4a) - a^2 + 2a + 1
Now, simplify further:
((2a^2 - 4a + 2) / a^2 - 4a^3 + 8a^2 - 4a - a^2 + 2a + 1
Collecting like terms:
(2 + 2) / a^2 - 3a^2 + 6a + 1
4 / a^2 - 3a^2 + 6a + 1
Therefore, the simplified expression is:
4 / a^2 - 3a^2 + 6a + 1.