1. **State the problem:** Simplify the expression $$\frac{6c(4u + 5)}{18c}$$. 2. **Identify the formula and rules:** We can simplify fractions by factoring and canceling common terms in numerator and denominator. 3. **Simplify step-by-step:** - The numerator is $$6c(4u + 5)$$. - The denominator is $$18c$$. 4. **Factor and cancel common terms:** - Factor numerator and denominator: $$\frac{6c(4u + 5)}{18c} = \frac{6c(4u + 5)}{18c}$$. - Cancel common factor $$6c$$ from numerator and denominator: $$\frac{6c(4u + 5)}{18c} = \frac{(4u + 5)}{3}$$ because $$18c = 6c \times 3$$. 5. **Final simplified expression:** $$\boxed{\frac{4u + 5}{3}}$$. This is the fully simplified form because no further common factors exist between numerator and denominator.