Solve for w A=lw+wh+lh

$A = l w + w h + l h$

Rewrite the equation as $l w + w h + l h = A$ .

$l w + w h + l h = A$

Subtract $l h$ from both sides of the equation.

$l w + w h = A - l h$

Factor $w$ out of $l w + w h$ .

Factor $w$ out of $l w$ .

$w l + w h = A - l h$

Factor $w$ out of $w h$ .

$w l + w (h) = A - l h$

Factor $w$ out of $w l + w (h)$ .

$w (l + h) = A - l h$

Divide each term in $w (l + h) = A - l h$ by $l + h$ and simplify.

Divide each term in $w (l + h) = A - l h$ by $l + h$ .

$\frac{w (l + h)}{l + h} = \frac{A}{l + h} + \frac{- l h}{l + h}$

Simplify the left side.

Cancel the common factor of $l + h$ .

Cancel the common factor.

$\frac{w (l + h)}{l + h} = \frac{A}{l + h} + \frac{- l h}{l + h}$

Divide $w$ by $1$ .

$w = \frac{A}{l + h} + \frac{- l h}{l + h}$

Simplify the right side.

Combine the numerators over the common denominator.

$w = \frac{A - l h}{l + h}$