Simplify (9-x^2)/(9x+27)

$\frac{9 - x^{2}}{9 x + 27}$

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{3^{2} - x^{2}}{9 x + 27}$

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

$\frac{(3 + x) (3 - x)}{9 x + 27}$

Simplify terms.

Factor $9$ out of $9 x + 27$ .

Factor $9$ out of $9 x$ .

$\frac{(3 + x) (3 - x)}{9 (x) + 27}$

Factor $9$ out of $27$ .

$\frac{(3 + x) (3 - x)}{9 x + 9 \cdot 3}$

Factor $9$ out of $9 x + 9 \cdot 3$ .

$\frac{(3 + x) (3 - x)}{9 (x + 3)}$

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

Reorder terms.

$\frac{(x + 3) (3 - x)}{9 (x + 3)}$

Cancel the common factor.

$\frac{(x + 3) (3 - x)}{9 (x + 3)}$

Rewrite the expression.

$\frac{3 - x}{9}$