Simplify (4x^2)/(2x-1)-1/(2x-1)

$\frac{4 x^{2}}{2 x - 1} - \frac{1}{2 x - 1}$

Combine the numerators over the common denominator.

$\frac{4 x^{2} - 1}{2 x - 1}$

Simplify the numerator.

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

$\frac{{(2 x)}^{2} - 1}{2 x - 1}$

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

$\frac{{(2 x)}^{2} - 1^{2}}{2 x - 1}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x$ and $b = 1$ .

$\frac{(2 x + 1) (2 x - 1)}{2 x - 1}$

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

$\frac{(2 x + 1) (2 x - 1)}{2 x - 1}$

Divide $2 x + 1$ by $1$ .

$2 x + 1$