Algebra Examples

$\frac{x - 2}{x - \frac{4}{x}}$

Step 1

Multiply the numerator and denominator of the fraction by $x$ .

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Step 1.1

Multiply $\frac{x - 2}{x - \frac{4}{x}}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{x - 2}{x - \frac{4}{x}}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Move the leading negative in $- \frac{4}{x}$ into the numerator.

$\frac{x \cdot x + x \cdot - 2}{x \cdot x + x \frac{- 4}{x}}$

Step 3.2

Cancel the common factor.

$\frac{x \cdot x + x \cdot - 2}{x \cdot x + x \frac{- 4}{x}}$

Step 3.3

Rewrite the expression.

$\frac{x \cdot x + x \cdot - 2}{x \cdot x - 4}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot - 2}{x \cdot x - 4}$

Step 4.2

Move $- 2$ to the left of $x$ .

$\frac{x^{2} - 2 \cdot x}{x \cdot x - 4}$

Step 4.3

Factor $x$ out of $x^{2} - 2 x$ .

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Step 4.3.1

Factor $x$ out of $x^{2}$ .

$\frac{x \cdot x - 2 x}{x \cdot x - 4}$

Step 4.3.2

Factor $x$ out of $- 2 x$ .

$\frac{x \cdot x + x \cdot - 2}{x \cdot x - 4}$

Step 4.3.3

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

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

Step 5

Simplify the denominator.

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Step 5.1

Raise $x$ to the power of $1$ .

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

Step 5.2

Raise $x$ to the power of $1$ .

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

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 5.4

Add $1$ and $1$ .

$\frac{x (x - 2)}{x^{2} - 4}$

Step 5.5

Rewrite $4$ as $2^{2}$ .

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

Step 5.6

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 $b = 2$ .

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

Step 6

Cancel the common factor of $x - 2$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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