1. **State the problem:** Perform the operation and combine into one fraction: $$\frac{2}{x-8} - \frac{7}{x}$$ 2. **Formula and rules:** To subtract fractions, find a common denominator, then combine the numerators over that denominator. 3. **Find the common denominator:** The denominators are $x-8$ and $x$, so the common denominator is $x(x-8)$. 4. **Rewrite each fraction with the common denominator:** $$\frac{2}{x-8} = \frac{2 \cdot x}{(x-8) \cdot x} = \frac{2x}{x(x-8)}$$ $$\frac{7}{x} = \frac{7 \cdot (x-8)}{x \cdot (x-8)} = \frac{7(x-8)}{x(x-8)}$$ 5. **Subtract the numerators:** $$\frac{2x}{x(x-8)} - \frac{7(x-8)}{x(x-8)} = \frac{2x - 7(x-8)}{x(x-8)}$$ 6. **Simplify the numerator:** $$2x - 7(x-8) = 2x - 7x + 56 = -5x + 56$$ 7. **Final combined fraction:** $$\frac{-5x + 56}{x(x-8)}$$ 8. **Optional:** Factor numerator if possible. Here, $-5x + 56 = -1(5x - 56)$, but this does not simplify with denominator. **Answer:** $$\frac{-5x + 56}{x(x-8)}$$