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

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

Step 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.

$x + b, 1$

Remove parentheses.

$x + b, 1$

The LCM of one and any expression is the expression.

$x + b$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $x + b$ .

Cancel the common factor.

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

Rewrite the expression.

$a = c (x + b)$

Simplify the right side.

Apply the distributive property.

$a = c x + c b$

Step 3

Solve the equation.

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

$c x + c b = a$

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

$c x = a - c b$

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

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

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

Simplify the left side.

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $- 1 b$ by $1$ .

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

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

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

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

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