To simplify the expression \((2m - 3) + (3n - 1) + (3m + 1)\), we will combine like terms.
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Group the like terms:
- The \(m\) terms: \(2m\) and \(3m\)
- The \(n\) terms: \(3n\)
- The constant terms: \(-3\), \(-1\), and \(+1\)
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Combine the terms:
- For \(m\): \(2m + 3m = 5m\)
- For \(n\): \(3n\)
- For constants: \(-3 - 1 + 1 = -3\)
Putting everything together, we get: \[ 5m + 3n - 3 \]
So, the simplified expression is: \[ \boxed{5m + 3n - 3} \]