Simplify (x^2-81)/(9+x)

$\frac{x^{2} - 81}{9 + x}$

Step 1

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

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

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 $b = 9$ .

$\frac{(x + 9) (x - 9)}{9 + x}$

Step 2

Cancel the common factor of $x + 9$ and $9 + x$ .

Reorder terms.

$\frac{(x + 9) (x - 9)}{x + 9}$

Cancel the common factor.

$\frac{(x + 9) (x - 9)}{x + 9}$

Divide $x - 9$ by $1$ .

$x - 9$