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

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

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

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

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

Simplify the left side.

Cancel the common factor of $a - x$ .

Cancel the common factor.

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

Rewrite the expression.

$x = b (a - x)$

Simplify the right side.

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

$x = b a - b x$

Step 3

Solve the equation.

Add $b x$ to both sides of the equation.

$x + b x = b a$

Factor $x$ out of $x + b x$ .

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

$x \cdot 1 + b x = b a$

Factor $x$ out of $b x$ .

$x \cdot 1 + x b = b a$

Factor $x$ out of $x \cdot 1 + x b$ .

$x (1 + b) = b a$

Divide each term in $x (1 + b) = b a$ by $1 + b$ and simplify.

Divide each term in $x (1 + b) = b a$ by $1 + b$ .

$\frac{x (1 + b)}{1 + b} = \frac{b a}{1 + b}$

Simplify the left side.

Cancel the common factor of $1 + b$ .

Cancel the common factor.

$\frac{x (1 + b)}{1 + b} = \frac{b a}{1 + b}$

Divide $x$ by $1$ .

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