To solve the expression

\[
38 - \left( \frac{8}{45} - \frac{17}{51} - \frac{3}{11} \right)
\]

let’s start by addressing the fractions:

1. **Finding a common denominator** for the fractions \(\frac{8}{45}\), \(\frac{17}{51}\), and \(\frac{3}{11}\). The least common multiple (LCM) of 45, 51, and 11 is 495.

2. **Convert each fraction**:
- For \(\frac{8}{45}\):
\[
\frac{8}{45} = \frac{8 \times 11}{45 \times 11} = \frac{88}{495}
\]
- For \(\frac{17}{51}\):
\[
\frac{17}{51} = \frac{17 \times 10}{51 \times 10} = \frac{170}{510} = \frac{170 \times 5}{510 \times 5} = \frac{850}{2550}
\]
- For \(\frac{3}{11}\):
\[
\frac{3}{11} = \frac{3 \times 45}{11 \times 45} = \frac{135}{495}
\]

3. **Combine the fractions in the parenthesis**:
- Calculate \(\frac{8}{45} - \frac{17}{51}\):
\[
\frac{88}{495} - \frac{170}{510} \to \frac{88}{495} - \frac{850}{2550} = \frac{88 - (850 \div 5)}{495} = \frac{-(762)}{495}
\]

4. Continuing, we subtract:
- Now, subtract \(\frac{3}{11}\) from the previous result:
\[
-\left(\frac{(762/495) + (135/495)}{}\right) = -\left(\frac{(762 + 135)}{495}\right)
\]

5. The main expression becomes:
- Therefore, we have:
\[
38 - \left(-\frac{(897)}{495}\right)
\]

Now combine the results, and simplify as necessary for your specific context.