Algebra Examples

$(5 x - 15) \div \frac{x^{2} - 9}{x + 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(5 x - 15) \frac{x + 2}{x^{2} - 9}$

Step 2

Simplify the denominator.

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Step 2.1

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

$(5 x - 15) \frac{x + 2}{x^{2} - 3^{2}}$

Step 2.2

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 $b = 3$ .

$(5 x - 15) \frac{x + 2}{(x + 3) (x - 3)}$

Step 3

Simplify terms.

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Step 3.1

Multiply $5 x - 15$ by $\frac{x + 2}{(x + 3) (x - 3)}$ .

$\frac{(5 x - 15) (x + 2)}{(x + 3) (x - 3)}$

Step 3.2

Factor $5$ out of $5 x - 15$ .

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Step 3.2.1

Factor $5$ out of $5 x$ .

$\frac{(5 (x) - 15) (x + 2)}{(x + 3) (x - 3)}$

Step 3.2.2

Factor $5$ out of $- 15$ .

$\frac{(5 x + 5 \cdot - 3) (x + 2)}{(x + 3) (x - 3)}$

Step 3.2.3

Factor $5$ out of $5 x + 5 \cdot - 3$ .

$\frac{5 (x - 3) (x + 2)}{(x + 3) (x - 3)}$

Step 3.3

Cancel the common factor of $x - 3$ .

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Step 3.3.1

Cancel the common factor.

$\frac{5 (x - 3) (x + 2)}{(x + 3) (x - 3)}$

Step 3.3.2

Rewrite the expression.

$\frac{5 (x + 2)}{x + 3}$