Algebra Examples

$\frac{3 x + 15}{x^{2} - 4} \div \frac{x + 5}{x - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x + 15}{x^{2} - 4} \cdot \frac{x - 2}{x + 5}$

Step 2

Factor $3$ out of $3 x + 15$ .

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 15}{x^{2} - 4} \cdot \frac{x - 2}{x + 5}$

Step 2.2

Factor $3$ out of $15$ .

$\frac{3 x + 3 \cdot 5}{x^{2} - 4} \cdot \frac{x - 2}{x + 5}$

Step 2.3

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

$\frac{3 (x + 5)}{x^{2} - 4} \cdot \frac{x - 2}{x + 5}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

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

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 $b = 2$ .

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

Step 4

Cancel the common factor of $x + 5$ .

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Step 4.1

Factor $x + 5$ out of $3 (x + 5)$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $x - 2$ .

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Step 5.1

Factor $x - 2$ out of $(x + 2) (x - 2)$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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