Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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 1.3.1

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

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

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Reorder terms.

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

Step 1.6

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

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Step 1.6.1

Subtract $x$ from $x$ .

$\frac{\frac{0 + 2}{x (x + 2)}}{2}$

Step 1.6.2

Add $0$ and $2$ .

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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