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

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

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

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

Simplify the left side.

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

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

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

Factor $- 1$ out of $a$ .

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

Factor $- 1$ out of $- b$ .

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

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

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

Cancel the common factor.

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

Divide $- 1$ by $1$ .

$x = - 1$