Pre-Algebra Examples

$\frac{x^{2} - 6 x - 9}{x + 3} \div \frac{x^{2} - 9}{3 (x + 3)}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 6 x - 9}{x + 3} \cdot \frac{3 (x + 3)}{x^{2} - 9}$

Step 2

Cancel the common factor of $x + 3$ .

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Step 2.1

Factor $x + 3$ out of $3 (x + 3)$ .

$\frac{x^{2} - 6 x - 9}{x + 3} \cdot \frac{(x + 3) \cdot 3}{x^{2} - 9}$

Step 2.2

Cancel the common factor.

$\frac{x^{2} - 6 x - 9}{x + 3} \cdot \frac{(x + 3) \cdot 3}{x^{2} - 9}$

Step 2.3

Rewrite the expression.

$(x^{2} - 6 x - 9) \frac{3}{x^{2} - 9}$

Step 3

Simplify the denominator.

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Step 3.1

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

$(x^{2} - 6 x - 9) \frac{3}{x^{2} - 3^{2}}$

Step 3.2

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 $b = 3$ .

$(x^{2} - 6 x - 9) \frac{3}{(x + 3) (x - 3)}$

Step 4

Multiply $x^{2} - 6 x - 9$ by $\frac{3}{(x + 3) (x - 3)}$ .

$\frac{(x^{2} - 6 x - 9) \cdot 3}{(x + 3) (x - 3)}$

Step 5

Move $3$ to the left of $x^{2} - 6 x - 9$ .

$\frac{3 (x^{2} - 6 x - 9)}{(x + 3) (x - 3)}$