1. **State the problem:** We want to write the expression $$\frac{7}{4} + \frac{5f}{3f+2}$$ as a single fraction in simplest form. 2. **Find a common denominator:** The denominators are 4 and $$3f+2$$. The common denominator is $$4(3f+2)$$. 3. **Rewrite each fraction with the common denominator:** $$\frac{7}{4} = \frac{7(3f+2)}{4(3f+2)}$$ $$\frac{5f}{3f+2} = \frac{5f \cdot 4}{(3f+2) \cdot 4} = \frac{20f}{4(3f+2)}$$ 4. **Add the fractions:** $$\frac{7(3f+2)}{4(3f+2)} + \frac{20f}{4(3f+2)} = \frac{7(3f+2) + 20f}{4(3f+2)}$$ 5. **Expand the numerator:** $$7(3f+2) + 20f = 21f + 14 + 20f = 41f + 14$$ 6. **Write the final single fraction:** $$\frac{41f + 14}{4(3f+2)}$$ 7. **Check for simplification:** The numerator and denominator have no common factors, so this is the simplest form. **Final answer:** $$\frac{41f + 14}{4(3f+2)}$$