Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify the denominator.

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Step 2.1

Write $1$ as a fraction with a common denominator.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Rewrite $\frac{x - 1 + 1}{x - 1}$ in a factored form.

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Step 2.3.1

Add $- 1$ and $1$ .

$\frac{1}{x - 1} \cdot \frac{1}{\frac{x + 0}{x - 1}}$

Step 2.3.2

Add $x$ and $0$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

Step 5

Cancel the common factor of $x - 1$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{1}{x}$