1. **State the problem:** Simplify the expression $$\frac{7c + \frac{y}{7c} - c - \frac{y}{c}}{x - c}$$. 2. **Rewrite the numerator:** Combine terms carefully: $$7c + \frac{y}{7c} - c - \frac{y}{c} = (7c - c) + \left(\frac{y}{7c} - \frac{y}{c}\right)$$ 3. **Simplify the integer terms:** $$7c - c = 6c$$ 4. **Find common denominator for the fractional terms:** The denominators are $7c$ and $c$. The common denominator is $7c$. Rewrite: $$\frac{y}{7c} - \frac{y}{c} = \frac{y}{7c} - \frac{7y}{7c} = \frac{y - 7y}{7c} = \frac{-6y}{7c}$$ 5. **Combine the numerator:** $$6c - \frac{6y}{7c}$$ 6. **Express as a single fraction:** Rewrite $6c$ as $\frac{42c^2}{7c}$ to have common denominator $7c$: $$\frac{42c^2}{7c} - \frac{6y}{7c} = \frac{42c^2 - 6y}{7c}$$ 7. **Rewrite the entire expression:** $$\frac{\frac{42c^2 - 6y}{7c}}{x - c} = \frac{42c^2 - 6y}{7c(x - c)}$$ 8. **Factor numerator if possible:** $$42c^2 - 6y = 6(7c^2 - y)$$ 9. **Final simplified form:** $$\frac{6(7c^2 - y)}{7c(x - c)}$$ This is the simplified expression.