Solve for x (1-a)x=a-1

$(1 - a) x = a - 1$

Step 1

Divide each term in $(1 - a) x = a - 1$ by $1 - a$ .

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

Step 2

Simplify the left side.

Cancel the common factor of $1 - a$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 3

Simplify the right side.

Combine the numerators over the common denominator.

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

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

Factor $- 1$ out of $a$ .

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

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

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Divide $- 1$ by $1$ .

$x = - 1$