Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Reorder the factors of $(x + 1) x$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $4$ by $1$ .

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

Step 4

Simplify terms.

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Step 4.1

Subtract $2 x$ from $4 x$ .

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

Step 4.2

Combine the numerators over the common denominator.

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

Step 4.3

Subtract $2$ from $4$ .

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

Step 4.4

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

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Step 4.4.1

Factor $2$ out of $2 x$ .

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

Step 4.4.2

Factor $2$ out of $2$ .

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

Step 4.4.3

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

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

Step 4.5

Cancel the common factor of $x + 1$ .

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Step 4.5.1

Cancel the common factor.

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

Step 4.5.2

Rewrite the expression.

$\frac{2}{x}$