1. **State the problem:** Solve the equation $$\frac{54}{h - 1} = 3$$ for $h$. 2. **Use the formula:** To solve for $h$, multiply both sides of the equation by the denominator $(h - 1)$ to eliminate the fraction. 3. **Multiply both sides:** $$\frac{54}{h - 1} \times (h - 1) = 3 \times (h - 1)$$ which simplifies to $$54 = 3(h - 1)$$ 4. **Distribute the 3:** $$54 = 3h - 3$$ 5. **Isolate $h$:** Add 3 to both sides: $$54 + 3 = 3h - 3 + 3$$ $$57 = 3h$$ 6. **Divide both sides by 3:** $$\frac{57}{\cancel{3}} = \frac{3h}{\cancel{3}}$$ $$19 = h$$ 7. **Final answer:** $$h = 19$$