Algebra Examples

$\frac{x^{2} - 1}{x}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $1$ as $1^{2}$ .

$\frac{x^{2} - 1^{2}}{x}$

Step 1.2

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 $b = 1$ .

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

Step 2

Expand $(x + 1) (x - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Move $- 1$ to the left of $x$ .

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

Step 3.1.3

Rewrite $- 1 x$ as $- x$ .

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

Step 3.1.4

Multiply $x$ by $1$ .

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

Step 3.1.5

Multiply $- 1$ by $1$ .

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

Step 3.2

Add $- x$ and $x$ .

$\frac{x^{2} + 0 - 1}{x}$

Step 3.3

Add $x^{2}$ and $0$ .

$\frac{x^{2} - 1}{x}$

Step 4

Split the fraction $\frac{x^{2} - 1}{x}$ into two fractions.

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

Step 5

Cancel the common factor of $x^{2}$ and $x$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Factor $x$ out of $x^{1}$ .

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

Step 5.2.3

Cancel the common factor.

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

Step 5.2.4

Rewrite the expression.

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

Step 5.2.5

Divide $x$ by $1$ .

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

Step 6

Move the negative in front of the fraction.

$x - \frac{1}{x}$