1. **State the problem:** Simplify the expression $\frac{2x - 5y}{6}$. 2. **Formula and rules:** When you have a fraction with a sum or difference in the numerator, you can write it as the sum or difference of two fractions: $$\frac{a - b}{c} = \frac{a}{c} - \frac{b}{c}$$ 3. **Apply the rule:** $$\frac{2x - 5y}{6} = \frac{2x}{6} - \frac{5y}{6}$$ 4. **Simplify each term:** $$\frac{2x}{6} = \frac{x}{3}$$ because 2 and 6 share a common factor 2. $$\frac{5y}{6}$$ cannot be simplified further. 5. **Final simplified expression:** $$\frac{x}{3} - \frac{5y}{6}$$ This is the simplified form of the original expression.