Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Cancel the common factor of $1 - x$ and $x - 1$ .

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Step 2.1

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 2.2

Factor $- 1$ out of $- x$ .

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

Step 2.3

Factor $- 1$ out of $- 1 (- 1) - (x)$ .

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

Step 2.4

Reorder terms.

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

Step 2.5

Cancel the common factor.

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

Step 2.6

Divide $- 1$ by $1$ .

$- 1$