Precalculus Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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 $b = x$ .

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

Step 2

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

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Step 2.1

Reorder terms.

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

$\frac{1}{3 - x}$