Trigonometry Examples

$\frac{\frac{4}{3 x + 6}}{2 + \frac{x}{x + 2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{3 x + 6} \cdot \frac{1}{2 + \frac{x}{x + 2}}$

Step 2

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

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{4}{3 (x) + 6} \cdot \frac{1}{2 + \frac{x}{x + 2}}$

Step 2.2

Factor $3$ out of $6$ .

$\frac{4}{3 x + 3 \cdot 2} \cdot \frac{1}{2 + \frac{x}{x + 2}}$

Step 2.3

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

$\frac{4}{3 (x + 2)} \cdot \frac{1}{2 + \frac{x}{x + 2}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$\frac{4}{3 (x + 2)} \cdot \frac{1}{\frac{2 (x + 2)}{x + 2} + \frac{x}{x + 2}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{4}{3 (x + 2)} \cdot \frac{1}{\frac{2 (x + 2) + x}{x + 2}}$

Step 3.3

Reorder terms.

$\frac{4}{3 (x + 2)} \cdot \frac{1}{\frac{x + 2 (x + 2)}{x + 2}}$

Step 3.4

Rewrite $\frac{x + 2 (x + 2)}{x + 2}$ in a factored form.

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Step 3.4.1

Apply the distributive property.

$\frac{4}{3 (x + 2)} \cdot \frac{1}{\frac{x + 2 x + 2 \cdot 2}{x + 2}}$

Step 3.4.2

Multiply $2$ by $2$ .

$\frac{4}{3 (x + 2)} \cdot \frac{1}{\frac{x + 2 x + 4}{x + 2}}$

Step 3.4.3

Add $x$ and $2 x$ .

$\frac{4}{3 (x + 2)} \cdot \frac{1}{\frac{3 x + 4}{x + 2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{3 (x + 2)} (1 \frac{x + 2}{3 x + 4})$

Step 5

Multiply $\frac{x + 2}{3 x + 4}$ by $1$ .

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

Step 6

Cancel the common factor of $x + 2$ .

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Step 6.1

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

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

$\frac{4}{3} \cdot \frac{1}{3 x + 4}$

Step 7

Multiply $\frac{4}{3}$ by $\frac{1}{3 x + 4}$ .

$\frac{4}{3 (3 x + 4)}$