1. **State the problem:** Simplify the expression $$\frac{6x^2 - 7x + 2}{4x^2 - 1}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor both numerator and denominator and then cancel any common factors. 3. **Factor the numerator:** $$6x^2 - 7x + 2$$ We look for two numbers that multiply to $6 \times 2 = 12$ and add to $-7$. These are $-3$ and $-4$. Rewrite: $$6x^2 - 3x - 4x + 2$$ Group: $$3x(2x - 1) - 2(2x - 1)$$ Factor out common binomial: $$(3x - 2)(2x - 1)$$ 4. **Factor the denominator:** $$4x^2 - 1$$ This is a difference of squares: $$ (2x)^2 - 1^2 = (2x - 1)(2x + 1) $$ 5. **Simplify the fraction:** $$\frac{(3x - 2)(2x - 1)}{(2x - 1)(2x + 1)}$$ Cancel the common factor $(2x - 1)$: $$\frac{3x - 2}{2x + 1}$$ 6. **Final answer:** $$\boxed{\frac{3x - 2}{2x + 1}}$$