Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $x$ .

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Step 3.2.1

Move the leading negative in $- \frac{1}{x}$ into the numerator.

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Simplify.

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Step 4.1

Multiply $x$ by $1$ .

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

Step 4.2

Multiply $x$ by $1$ .

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