To solve the expression:

$-9 \frac{1}{2} + 8 \frac{3}{4} + \frac{3}{4}$

1. Convert the mixed numbers into improper fractions:

   • $-9 \frac{1}{2} = -\frac{19}{2}$
   • $8 \frac{3}{4} = \frac{35}{4}$
   • $\frac{3}{4}$ remains as $\frac{3}{4}$

2. The fractions need a common denominator to add them. The common denominator of 2 and 4 is 4. So:

   $-\frac{19}{2} = -\frac{38}{4}$

   Now the expression becomes:

   $-\frac{38}{4} + \frac{35}{4} + \frac{3}{4}$

3. Add the fractions:

   $\left(-\frac{38}{4} + \frac{35}{4} + \frac{3}{4}\right) = \frac{-38 + 35 + 3}{4} = \frac{0}{4} = 0$

So, the result is:

$\boxed{0}$

Would you like further details or have any questions?

Here are some related questions you might find interesting:

1. How do you simplify mixed numbers?
2. How do you find the least common denominator between fractions?
3. What are improper fractions, and how do you convert them back to mixed numbers?
4. How can you add and subtract negative and positive numbers effectively?
5. How do you perform operations with fractions?

Tip: Always convert mixed numbers to improper fractions before adding or subtracting.