Solve for b a/(a+b)=c

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

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 $\frac{a}{a + b} = c$ by $a + b$ to eliminate the fractions.

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

$\frac{a}{a + b} (a + b) = c (a + b)$

Simplify the left side.

Cancel the common factor of $a + b$ .

Cancel the common factor.

$\frac{a}{a + b} (a + b) = c (a + b)$

Rewrite the expression.

$a = c (a + b)$

Simplify the right side.

Apply the distributive property.

$a = c a + c b$

Solve the equation.

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

$c a + c b = a$

Subtract $c a$ from both sides of the equation.

$c b = a - c a$

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

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

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

Simplify the left side.

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $- 1 a$ by $1$ .

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

Rewrite $- 1 a$ as $- a$ .

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