Solve for b -ab+a=b-1

$- a b + a = b - 1$

Step 1

Subtract $b$ from both sides of the equation.

$- a b + a - b = - 1$

Step 2

Subtract $a$ from both sides of the equation.

$- a b - b = - 1 - a$

Step 3

Factor $b$ out of $- a b - b$ .

Factor $b$ out of $- a b$ .

$b (- a) - b = - 1 - a$

Factor $b$ out of $- b$ .

$b (- a) + b \cdot - 1 = - 1 - a$

Factor $b$ out of $b (- a) + b \cdot - 1$ .

$b (- a - 1) = - 1 - a$

Step 4

Divide each term in $b (- a - 1) = - 1 - a$ by $- a - 1$ and simplify.

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

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

Simplify the left side.

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

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

$b = 1$