1. **State the problem:** Rearrange the formula $$y = \frac{3x - 2}{x + 1}$$ to make $$x$$ the subject. 2. **Start with the given equation:** $$y = \frac{3x - 2}{x + 1}$$ 3. **Multiply both sides by the denominator to eliminate the fraction:** $$y(x + 1) = 3x - 2$$ 4. **Expand the left side:** $$yx + y = 3x - 2$$ 5. **Group all terms involving $$x$$ on one side and constants on the other:** $$yx - 3x = -2 - y$$ 6. **Factor out $$x$$ on the left side:** $$x(y - 3) = -2 - y$$ 7. **Divide both sides by $$y - 3$$ to isolate $$x$$:** $$x = \frac{-2 - y}{y - 3}$$ 8. **Simplify the numerator by factoring out a negative sign:** $$x = \frac{-(2 + y)}{y - 3} = \frac{y + 2}{3 - y}$$ **Final answer:** $$x = \frac{y + 2}{3 - y}$$