Solve for b P=a+(n-1)b

$P = a + (n - 1) b$

Rewrite the equation as $a + (n - 1) b = P$ .

$a + (n - 1) b = P$

Simplify each term.

Apply the distributive property.

$a + n b - 1 b = P$

Rewrite $- 1 b$ as $- b$ .

$a + n b - b = P$

Subtract $a$ from both sides of the equation.

$n b - b = P - a$

Factor $b$ out of $n b - b$ .

Factor $b$ out of $n b$ .

$b n - b = P - a$

Factor $b$ out of $- b$ .

$b n + b \cdot - 1 = P - a$

Factor $b$ out of $b n + b \cdot - 1$ .

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

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

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

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

Simplify the left side.

Cancel the common factor of $n - 1$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Combine the numerators over the common denominator.

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