Solve for L S=(L(a+b))/2

$S = \frac{L (a + b)}{2}$

Rewrite the equation as $\frac{L (a + b)}{2} = S$ .

$\frac{L (a + b)}{2} = S$

Multiply both sides of the equation by $2$ .

$2 \frac{L (a + b)}{2} = 2 S$

Simplify the left side.

Simplify $2 \frac{L (a + b)}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{L (a + b)}{2} = 2 S$

Rewrite the expression.

$L (a + b) = 2 S$

Apply the distributive property.

$L a + L b = 2 S$

Factor $L$ out of $L a + L b$ .

Factor $L$ out of $L a$ .

$L (a) + L b = 2 S$

Factor $L$ out of $L b$ .

$L (a) + L (b) = 2 S$

Factor $L$ out of $L (a) + L (b)$ .

$L (a + b) = 2 S$

Divide each term in $L (a + b) = 2 S$ by $a + b$ and simplify.

Divide each term in $L (a + b) = 2 S$ by $a + b$ .

$\frac{L (a + b)}{a + b} = \frac{2 S}{a + b}$

Simplify the left side.

Cancel the common factor of $a + b$ .

Cancel the common factor.

$\frac{L (a + b)}{a + b} = \frac{2 S}{a + b}$

Divide $L$ by $1$ .

$L = \frac{2 S}{a + b}$