1. **State the problem:** Simplify the expression $$3 - \frac{x - 1}{\frac{x^2 - 1}{3x + 2}}$$ and write it in the form $$\frac{a}{x + b}$$ where $a$ and $b$ are integers. 2. **Rewrite the expression:** Division by a fraction is multiplication by its reciprocal, so $$3 - \frac{x - 1}{\frac{x^2 - 1}{3x + 2}} = 3 - (x - 1) \times \frac{3x + 2}{x^2 - 1}$$ 3. **Factor the denominator:** Note that $$x^2 - 1 = (x - 1)(x + 1)$$, so $$3 - (x - 1) \times \frac{3x + 2}{(x - 1)(x + 1)}$$ 4. **Cancel common factors:** The $(x - 1)$ terms cancel: $$3 - \cancel{(x - 1)} \times \frac{3x + 2}{\cancel{(x - 1)}(x + 1)} = 3 - \frac{3x + 2}{x + 1}$$ 5. **Rewrite 3 as a fraction:** $$3 = \frac{3(x + 1)}{x + 1} = \frac{3x + 3}{x + 1}$$ 6. **Combine the fractions:** $$\frac{3x + 3}{x + 1} - \frac{3x + 2}{x + 1} = \frac{(3x + 3) - (3x + 2)}{x + 1}$$ 7. **Simplify the numerator:** $$(3x + 3) - (3x + 2) = 3x + 3 - 3x - 2 = 1$$ 8. **Final simplified form:** $$\frac{1}{x + 1}$$ Thus, the expression can be written as $$\frac{a}{x + b}$$ with $a = 1$ and $b = 1$. **Answer:** $a = 1$, $b = 1$