Solve for b c/(a-b)=1

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

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a - b, 1$

Remove parentheses.

$a - b, 1$

The LCM of one and any expression is the expression.

$a - b$

Multiply each term in $\frac{c}{a - b} = 1$ by $a - b$ to eliminate the fractions.

Multiply each term in $\frac{c}{a - b} = 1$ by $a - b$ .

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

Simplify the left side.

Cancel the common factor of $a - b$ .

Cancel the common factor.

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

Rewrite the expression.

$c = 1 (a - b)$

Simplify the right side.

Multiply $a - b$ by $1$ .

$c = a - b$

Solve the equation.

Rewrite the equation as $a - b = c$ .

$a - b = c$

Subtract $a$ from both sides of the equation.

$- b = c - a$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{c}{- 1}$ .

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

Rewrite $- 1 \cdot c$ as $- c$ .

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

Dividing two negative values results in a positive value.

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

Divide $a$ by $1$ .

$b = - c + a$