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

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

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.

$1, c, 1$

The LCM of one and any expression is the expression.

$c$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $c$ .

Move the leading negative in $- \frac{b x}{c}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$x c - b x = a c$

Step 3

Solve the equation.

Factor $x$ out of $x c - b x$ .

Factor $x$ out of $x c$ .

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

Factor $x$ out of $- b x$ .

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

Factor $x$ out of $x (c) + x (- b)$ .

$x (c - b) = a c$

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

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

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

Simplify the left side.

Cancel the common factor of $c - b$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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