Trigonometry Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Factor $x$ out of $3 x$ .

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

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

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

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 $b = 3$ .

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x + 3$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

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

$3 (x - 3)$

Step 4.2

Apply the distributive property.

$3 x + 3 \cdot - 3$

Step 4.3

Multiply $3$ by $- 3$ .

$3 x - 9$