Combine the following expressions. \( 4 m+5 \sqrt{n}-m+6 m-3 \sqrt{n} \) \( 9 m+2 \sqrt{n} \) \( 9 m-2 \sqrt{n} \) \( 11 m+2 \sqrt{n} \)

Let’s start by combining the first expression: \( 4m + 5\sqrt{n} - m + 6m - 3\sqrt{n} \). Combine like terms for \( m \): \( (4m - m + 6m) \) results in \( 9m \). Now, for \( \sqrt{n} \): \( (5\sqrt{n} - 3\sqrt{n}) \) simplifies to \( 2\sqrt{n} \). Thus, the first expression combines to: \( 9m + 2\sqrt{n} \). Next, we can add this result to the other two expressions. Adding \( 9m + 2\sqrt{n} \) to \( 9m + 2\sqrt{n} \): \[ (9m + 2\sqrt{n}) + (9m + 2\sqrt{n}) = 18m + 4\sqrt{n} \] Now, combining with \( 11m + 2\sqrt{n} \): \[ (18m + 4\sqrt{n}) + (11m + 2\sqrt{n}) = (18m + 11m) + (4\sqrt{n} + 2\sqrt{n}) = 29m + 6\sqrt{n} \] So, the final result after combining all the expressions is: \[ 29m + 6\sqrt{n} \]