Divide (2ab-a)÷(4b^2-4b+1)

$(2 a b - a) \div (4 b^{2} - 4 b + 1)$

Rewrite the division as a fraction.

$\frac{2 a b - a}{4 b^{2} - 4 b + 1}$

Factor $a$ out of $2 a b - a$ .

Factor $a$ out of $2 a b$ .

$\frac{a (2 b) - a}{4 b^{2} - 4 b + 1}$

Factor $a$ out of $- a$ .

$\frac{a (2 b) + a \cdot - 1}{4 b^{2} - 4 b + 1}$

Factor $a$ out of $a (2 b) + a \cdot - 1$ .

$\frac{a (2 b - 1)}{4 b^{2} - 4 b + 1}$

Factor using the perfect square rule.

Rewrite $4 b^{2}$ as ${(2 b)}^{2}$ .

$\frac{a (2 b - 1)}{{(2 b)}^{2} - 4 b + 1}$

Rewrite $1$ as $1^{2}$ .

$\frac{a (2 b - 1)}{{(2 b)}^{2} - 4 b + 1^{2}}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 b = 2 \cdot (2 b) \cdot 1$

Rewrite the polynomial.

$\frac{a (2 b - 1)}{{(2 b)}^{2} - 2 \cdot (2 b) \cdot 1 + 1^{2}}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 b$ and $b = 1$ .

$\frac{a (2 b - 1)}{{(2 b - 1)}^{2}}$

Cancel the common factor of $2 b - 1$ and ${(2 b - 1)}^{2}$ .

Factor $2 b - 1$ out of $a (2 b - 1)$ .

$\frac{(2 b - 1) a}{{(2 b - 1)}^{2}}$

Cancel the common factors.

Factor $2 b - 1$ out of ${(2 b - 1)}^{2}$ .

$\frac{(2 b - 1) a}{(2 b - 1) (2 b - 1)}$

Cancel the common factor.

$\frac{(2 b - 1) a}{(2 b - 1) (2 b - 1)}$

Rewrite the expression.

$\frac{a}{2 b - 1}$