1. **State the problem:** Solve the equation $$\frac{1}{k} + \frac{5}{12} = \frac{6}{5}$$ for $k$. 2. **Isolate the term with $k$:** Subtract $\frac{5}{12}$ from both sides: $$\frac{1}{k} + \frac{5}{12} - \frac{5}{12} = \frac{6}{5} - \frac{5}{12}$$ which simplifies to $$\frac{1}{k} = \frac{6}{5} - \frac{5}{12}$$ 3. **Find a common denominator to subtract the fractions on the right:** The least common denominator of 5 and 12 is 60. $$\frac{6}{5} = \frac{6 \times 12}{5 \times 12} = \frac{72}{60}$$ $$\frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60}$$ So, $$\frac{1}{k} = \frac{72}{60} - \frac{25}{60} = \frac{72 - 25}{60} = \frac{47}{60}$$ 4. **Solve for $k$ by taking the reciprocal:** $$k = \frac{1}{\frac{47}{60}} = \frac{60}{47}$$ 5. **Final answer:** $$k = \frac{60}{47}$$ This is the exact value of $k$.