Solve for x g=(x-c)/x ; for x

$g = \frac{x - c}{x}$ ; for $x$

Step 1

Rewrite the equation as $\frac{x - c}{x} = g$ .

$\frac{x - c}{x} = g$

Step 2

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.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Step 3

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

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

$\frac{x - c}{x} x = g x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x - c}{x} x = g x$

Rewrite the expression.

$x - c = g x$

Step 4

Solve the equation.

Subtract $g x$ from both sides of the equation.

$x - c - g x = 0$

Add $c$ to both sides of the equation.

$x - g x = c$

Factor $x$ out of $x - g x$ .

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - g x = c$

Factor $x$ out of $- g x$ .

$x \cdot 1 + x (- g) = c$

Factor $x$ out of $x \cdot 1 + x (- g)$ .

$x (1 - g) = c$

Divide each term in $x (1 - g) = c$ by $1 - g$ and simplify.

Divide each term in $x (1 - g) = c$ by $1 - g$ .

$\frac{x (1 - g)}{1 - g} = \frac{c}{1 - g}$

Simplify the left side.

Cancel the common factor of $1 - g$ .

Cancel the common factor.

$\frac{x (1 - g)}{1 - g} = \frac{c}{1 - g}$

Divide $x$ by $1$ .

$x = \frac{c}{1 - g}$