1. **State the problem:** Solve the equation $$\frac{45 - x}{x} = 4$$ for $x$. 2. **Formula and rules:** This is a rational equation where the variable $x$ is in the denominator. To solve, multiply both sides by $x$ to eliminate the denominator, but remember $x \neq 0$. 3. **Multiply both sides by $x$:** $$\frac{45 - x}{x} \times x = 4 \times x$$ which simplifies to $$45 - x = 4x$$ 4. **Solve for $x$:** Add $x$ to both sides: $$45 = 4x + x$$ $$45 = 5x$$ 5. **Divide both sides by 5:** $$x = \frac{45}{5}$$ $$x = 9$$ 6. **Check the solution:** Substitute $x=9$ back into the original equation: $$\frac{45 - 9}{9} = \frac{36}{9} = 4$$ which is true. **Final answer:** $$x = 9$$