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To find the difference between the two expressions, we can subtract them.
(3x ^ 2 - x - 1) - (- 3x ^ 2 - 1)
= 3x ^ 2 - x - 1 + 3x ^ 2 + 1
= 3x ^ 2 + 3x ^ 2 - x - 1 + 1
= 6x ^ 2 - x
Therefore, the difference of the expression is 6x ^ 2 - x.