Solve for x x/(a-x)=1

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

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 $\frac{x}{a - x} = 1$ by $a - x$ to eliminate the fractions.

Multiply each term in $\frac{x}{a - x} = 1$ by $a - x$ .

$\frac{x}{a - x} (a - x) = 1 (a - x)$

Simplify the left side.

Cancel the common factor of $a - x$ .

Cancel the common factor.

$\frac{x}{a - x} (a - x) = 1 (a - x)$

Rewrite the expression.

$x = 1 (a - x)$

Simplify the right side.

Multiply $a - x$ by $1$ .

$x = a - x$

Step 3

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$x + x = a$

Add $x$ and $x$ .

$2 x = a$

Divide each term in $2 x = a$ by $2$ and simplify.

Divide each term in $2 x = a$ by $2$ .

$\frac{2 x}{2} = \frac{a}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{a}{2}$

Divide $x$ by $1$ .

$x = \frac{a}{2}$