1. **State the problem:** We need to find the variable $m$ from the equation $$\frac{k}{m} + \frac{x}{y} = p.$$\n\n2. **Isolate the term with $m$:** Subtract $\frac{x}{y}$ from both sides to isolate $\frac{k}{m}$:\n$$\frac{k}{m} = p - \frac{x}{y}.$$\n\n3. **Rewrite the right side with a common denominator:**\n$$p - \frac{x}{y} = \frac{py}{y} - \frac{x}{y} = \frac{py - x}{y}.$$\n\n4. **Substitute back:**\n$$\frac{k}{m} = \frac{py - x}{y}.$$\n\n5. **Solve for $m$ by cross-multiplying:**\n$$k \cdot y = m \cdot (py - x).$$\n\n6. **Isolate $m$:**\n$$m = \frac{ky}{py - x}.$$\n\n**Final answer:** $$m = \frac{ky}{py - x}.$$