Simplify (x^2)/(2x-3)-4/(2x-3)

$\frac{x^{2}}{2 x - 3} - \frac{4}{2 x - 3}$

Step 1

Combine the numerators over the common denominator.

$\frac{x^{2} - 4}{2 x - 3}$

Step 2

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{x^{2} - 2^{2}}{2 x - 3}$

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

$\frac{(x + 2) (x - 2)}{2 x - 3}$