Add: (2m−3)+(3n−1)+(3m+1)

To add the expressions \( (2m - 3) + (3n - 1) + (3m + 1) \), we can combine like terms.

1. Combine the \( m \) terms: \[ 2m + 3m = 5m \]

2. Combine the \( n \) terms: \[ 3n \quad (\text{there is no other } n \text{ term to combine with}) \]

3. Combine the constant terms: \[ -3 - 1 + 1 = -3 \]

Putting it all together, the expression simplifies to: \[ 5m + 3n - 3 \]

Therefore, the final result is: \[ \boxed{5m + 3n - 3} \]