Pre-Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{1 - x}{1 - x}$ .

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

Step 3

Combine $- 1$ and $\frac{1 - x}{1 - x}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $- 1$ by $1$ .

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

Step 5.3

Multiply $- - x$ .

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Step 5.3.1

Multiply $- 1$ by $- 1$ .

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

Step 5.3.2

Multiply $x$ by $1$ .

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

Step 5.4

Subtract $1$ from $1$ .

$\frac{0 + x}{1 - x} (1 - x)$

Step 5.5

Add $0$ and $x$ .

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

Step 6

Cancel the common factor of $1 - x$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$x$