1. **State the problem:** Make $x$ the subject of the equation $$y = \frac{3x + 2}{x - 1}$$. 2. **Understand the formula:** We want to isolate $x$ on one side of the equation. 3. **Multiply both sides by the denominator to eliminate the fraction:** $$y(x - 1) = 3x + 2$$ 4. **Distribute $y$ on the left side:** $$yx - y = 3x + 2$$ 5. **Group all terms involving $x$ on one side and constants on the other:** $$yx - 3x = y + 2$$ 6. **Factor out $x$ on the left side:** $$x(y - 3) = y + 2$$ 7. **Divide both sides by $(y - 3)$ to solve for $x$:** $$x = \frac{y + 2}{y - 3}$$ **Final answer:** $$x = \frac{y + 2}{y - 3}$$