Question: User: $\frac{1}{x-3}=4$
1. **State the problem:** Solve the equation $$\frac{1}{x-3} = 4$$ for $x$.
2. **Use the formula:** To solve for $x$, multiply both sides by the denominator to eliminate the fraction.
3. **Multiply both sides:**
$$\cancel{(x-3)} \times \frac{1}{\cancel{x-3}} = 4 \times (x-3)$$
which simplifies to
$$1 = 4(x-3)$$
4. **Distribute the 4:**
$$1 = 4x - 12$$
5. **Add 12 to both sides:**
$$1 + 12 = 4x - 12 + 12$$
$$13 = 4x$$
6. **Divide both sides by 4:**
$$\frac{13}{\cancel{4}} = \frac{4x}{\cancel{4}}$$
which simplifies to
$$x = \frac{13}{4}$$
7. **Final answer:**
$$x = \frac{13}{4}$$