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

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

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.

$a - x, 1$

Remove parentheses.

$a - x, 1$

The LCM of one and any expression is the expression.

$a - x$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $a - x$ .

Cancel the common factor.

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

Rewrite the expression.

$b = c (a - x)$

Simplify the right side.

Apply the distributive property.

$b = c a + c (- x)$

Rewrite using the commutative property of multiplication.

$b = c a - c x$

Step 3

Solve the equation.

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

$c a - c x = b$

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

$- c x = b - c a$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

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

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