43 5/8 + (-25 1/6)

To solve \( 43 \frac{5}{8} + (-25 \frac{1}{6}) \), we can first convert the mixed numbers into improper fractions.

1. Convert \( 43 \frac{5}{8} \) into an improper fraction.

\[ 43 \frac{5}{8} = \frac{(43 \times 8) + 5}{8} = \frac{344 + 5}{8} = \frac{349}{8} \]

2. Convert \( -25 \frac{1}{6} \) into an improper fraction.

\[ -25 \frac{1}{6} = -\left(\frac{(25 \times 6) + 1}{6}\right) = -\left(\frac{150 + 1}{6}\right) = -\frac{151}{6} \]

3. Now we need to add these two fractions:

\[ \frac{349}{8} + \left(-\frac{151}{6}\right) = \frac{349}{8} - \frac{151}{6} \]

To add these fractions, we need a common denominator. The least common multiple of 8 and 6 is 24.

4. Convert the fractions to have a denominator of 24.

\[ \frac{349}{8} = \frac{349 \times 3}{8 \times 3} = \frac{1047}{24} \] \[ -\frac{151}{6} = -\frac{151 \times 4}{6 \times 4} = -\frac{604}{24} \]

5. Now we can add the fractions:

\[ \frac{1047}{24} - \frac{604}{24} = \frac{1047 - 604}{24} = \frac{443}{24} \]

6. Finally, convert back to a mixed number if necessary.

\[ \frac{443}{24} = 18 \frac{11}{24} \]

Thus, the answer is:

\[ \boxed{18 \frac{11}{24}} \]