1. **State the problem:** Simplify the complex fraction $$\frac{\frac{2}{x} + 7}{8}$$. 2. **Rewrite the numerator:** The numerator is $$\frac{2}{x} + 7$$. To combine these terms, write 7 as $$\frac{7x}{x}$$ to have a common denominator: $$\frac{2}{x} + 7 = \frac{2}{x} + \frac{7x}{x} = \frac{2 + 7x}{x}$$ 3. **Rewrite the entire fraction:** Now the complex fraction becomes: $$\frac{\frac{2 + 7x}{x}}{8}$$ 4. **Divide by 8:** Dividing by 8 is the same as multiplying by $$\frac{1}{8}$$, so: $$\frac{2 + 7x}{x} \times \frac{1}{8} = \frac{2 + 7x}{8x}$$ 5. **Final simplified form:** $$\boxed{\frac{2 + 7x}{8x}}$$ This is the simplified form of the given complex fraction.