(4x² - 4x + 1) ÷ (2x - 1) is equal to :

1. 2x + 1

2. 2x - 1

3. 2^x - 1

4. none of these

(4x² - 4x + 1) ÷ (2x - 1)

= $\dfrac{(4x^2 - 4x + 1)}{(2x - 1)}$

Using the formula,

[∵ (x - y)² = x² + y² - 2xy]

= $\dfrac{((2x)^2 - 2 \times 2x \times 1 + 1)}{(2x - 1)}$

= $\dfrac{(2x - 1)^2}{(2x - 1)}$

= $\dfrac{(2x - 1)(2x - 1)}{(2x - 1)}$

= $\dfrac{(2x - 1)\cancel{(2x - 1)}}{\cancel{(2x - 1)}}$

= 2x - 1

Hence, option 2 is the correct option.