Simplify (9-x^2)/(27-x^3)

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

Simplify the numerator.

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

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

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

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

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

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

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

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

Raise $3$ to the power of $2$ .

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

Cancel the common factor of $3 - x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (9-x^2)/(27-x^3)

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