Perform the following additions and/or subtractions: \( \left(5 u^{4}-8 u^{2}-2\right)-\left(-6 u^{4}+3 u^{2}+1\right)=\square \)

To solve the expression \( \left(5 u^{4}-8 u^{2}-2\right)-\left(-6 u^{4}+3 u^{2}+1\right) \), we will first distribute the negative sign across the second expression: \[ 5 u^{4} - 8 u^{2} - 2 + 6 u^{4} - 3 u^{2} - 1 \] Next, we combine like terms. Start with the \( u^{4} \) terms: \[ 5 u^{4} + 6 u^{4} = 11 u^{4} \] Now, combine the \( u^{2} \) terms: \[ -8 u^{2} - 3 u^{2} = -11 u^{2} \] Finally, combine the constant terms: \[ -2 - 1 = -3 \] Putting it all together, we have: \[ 11 u^{4} - 11 u^{2} - 3 \] Thus, the final result is: \[ \boxed{11 u^{4} - 11 u^{2} - 3} \]