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

$(a - b) x = b - a$

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

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

Simplify the left side.

Cancel the common factor of $a - b$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

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

Factor $- 1$ out of $b$ .

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

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

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Divide $- 1$ by $1$ .

$x = - 1$