Trigonometry Examples

$\frac{1}{x} + \frac{1}{x + 2}$

Step 1

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

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

Step 2

To write $\frac{1}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Step 3

Write each expression with a common denominator of $x (x + 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Reorder the factors of $(x + 2) x$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Add $x$ and $x$ .

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

Step 5.2

Factor $2$ out of $2 x + 2$ .

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Step 5.2.1

Factor $2$ out of $2 x$ .

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

Step 5.2.2

Factor $2$ out of $2$ .

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

Step 5.2.3

Factor $2$ out of $2 (x) + 2 (1)$ .

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