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

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

Step 1

Rewrite the equation as $\frac{x}{a - b} = w$ .

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

Step 2

Multiply both sides by $a - b$ .

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

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $a - b$ .

Cancel the common factor.

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

Rewrite the expression.

$x = w (a - b)$

Simplify the right side.

Simplify $w (a - b)$ .

Apply the distributive property.

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

$x = w a - w b$

Reorder $w$ and $a$ .

$x = a w - w b$

Move $w$ .

$x = a w - b w$