Algebra Examples

$\frac{\frac{3 x + 6}{x + 5}}{\frac{x + 2}{x^{2} - 25}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 x + 6}{x + 5} \cdot \frac{x^{2} - 25}{x + 2}$

Step 2

Simplify terms.

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Step 2.1

Factor $3$ out of $3 x + 6$ .

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Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 6}{x + 5} \cdot \frac{x^{2} - 25}{x + 2}$

Step 2.1.2

Factor $3$ out of $6$ .

$\frac{3 x + 3 \cdot 2}{x + 5} \cdot \frac{x^{2} - 25}{x + 2}$

Step 2.1.3

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{3 (x + 2)}{x + 5} \cdot \frac{x^{2} - 25}{x + 2}$

Step 2.2

Cancel the common factor of $x + 2$ .

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Step 2.2.1

Factor $x + 2$ out of $3 (x + 2)$ .

$\frac{(x + 2) \cdot 3}{x + 5} \cdot \frac{x^{2} - 25}{x + 2}$

Step 2.2.2

Cancel the common factor.

$\frac{(x + 2) \cdot 3}{x + 5} \cdot \frac{x^{2} - 25}{x + 2}$

Step 2.2.3

Rewrite the expression.

$\frac{3}{x + 5} (x^{2} - 25)$

Step 2.3

Multiply $\frac{3}{x + 5}$ by $x^{2} - 25$ .

$\frac{3 (x^{2} - 25)}{x + 5}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $25$ as $5^{2}$ .

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

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 $b = 5$ .

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x + 5$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Divide $3 (x - 5)$ by $1$ .

$3 (x - 5)$

Step 4.2

Apply the distributive property.

$3 x + 3 \cdot - 5$

Step 4.3

Multiply $3$ by $- 5$ .

$3 x - 15$