To simplify $(3x^2 - x - 1) - (-3x^2 - 1)$, we start by distributing the negative sign across the terms in the second polynomial:

$(3x^2 - x - 1) - (-3x^2 - 1) = 3x^2 - x - 1 + 3x^2 + 1$

Next, combine like terms:

1. Combine $3x^2 + 3x^2$: $6x^2$
2. Combine $-x$: $-x$ (no similar terms)
3. Combine $-1 + 1$: $0$

The resulting expression is:

$6x^2 - x$

Final Answer:

$6x^2 - x$

Would you like me to explain further or verify? Here are some related questions for practice:

1. Simplify $(4x^2 - 2x + 3) - (2x^2 - 3x - 5)$.
2. Expand and simplify $(2x - 3)(3x + 4)$.
3. Simplify $(5x - 2) - (3x - 7)$.
4. Solve for $x$ in the equation $6x^2 - x = 0$.
5. Factor $6x^2 - x$.

Tip: When subtracting polynomials, carefully distribute the negative sign to avoid sign errors.