To solve the expression \((\frac{3}{8} + (-\frac{3}{4}) + \frac{7}{12}) \div \frac{5}{6} + \frac{1}{2}\), we need to follow the order of operations (PEMDAS/BODMAS). Let's break it down step by step.

1. **Inside the parentheses**: \(\frac{3}{8} + (-\frac{3}{4}) + \frac{7}{12}\)

First, we need a common denominator to add these fractions. The least common multiple of 8, 4, and 12 is 24.

- Convert \(\frac{3}{8}\) to a fraction with a denominator of 24:
\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\]

- Convert \(-\frac{3}{4}\) to a fraction with a denominator of 24:
\[
-\frac{3}{4} = -\frac{3 \times 6}{4 \times 6} = -\frac{18}{24}
\]

- Convert \(\frac{7}{12}\) to a fraction with a denominator of 24:
\[
\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}
\]

Now, add the fractions:
\[
\frac{9}{24} + (-\frac{18}{24}) + \frac{14}{24} = \frac{9 - 18 + 14}{24} = \frac{5}{24}
\]

2. **Division**: \(\frac{5}{24} \div \frac{5}{6}\)

To divide by a fraction, multiply by its reciprocal:
\[
\frac{5}{24} \div \frac{5}{6} = \frac{5}{24} \times \frac{6}{5}
\]

Simplify the multiplication:
\[
\frac{5 \times 6}{24 \times 5} = \frac{30}{120} = \frac{1}{4}
\]

3. **Addition**: \(\frac{1}{4} + \frac{1}{2}\)

Convert \(\frac{1}{2}\) to a fraction with a denominator of 4:
\[
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\]

Now, add the fractions:
\[
\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}
\]

So, the final result is:
\[
\frac{3}{4}
\]