Divide (9x^2-y^2)÷(3x+y)

$(9 x^{2} - y^{2}) \div (3 x + y)$

Rewrite the division as a fraction.

$\frac{9 x^{2} - y^{2}}{3 x + y}$

Simplify the numerator.

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = y$ .

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

Cancel the common factor of $3 x + y$ .

Cancel the common factor.

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

Divide $3 x - y$ by $1$ .

$3 x - y$