Solve for a a=(a+b)/2h

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

Simplify $\frac{a + b}{2} \cdot h$ .

Combine $\frac{a + b}{2}$ and $h$ .

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

Reorder factors in $\frac{(a + b) h}{2}$ .

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

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

Subtract $\frac{h (a + b)}{2}$ from both sides of the equation.

$a - \frac{h (a + b)}{2} = 0$

To write $a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a \cdot \frac{2}{2} - \frac{h (a + b)}{2} = 0$

Combine $a$ and $\frac{2}{2}$ .

$\frac{a \cdot 2}{2} - \frac{h (a + b)}{2} = 0$

Combine the numerators over the common denominator.

$\frac{a \cdot 2 - h (a + b)}{2} = 0$

Simplify the numerator.

Move $2$ to the left of $a$ .

$\frac{2 \cdot a - h (a + b)}{2} = 0$

Apply the distributive property.

$\frac{2 a - h a - h b}{2} = 0$

Set the numerator equal to zero.

$2 a - h a - h b = 0$

Solve the equation for $a$ .

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

$2 a - h a = h b$

Factor $a$ out of $2 a - h a$ .

Factor $a$ out of $2 a$ .

$a \cdot 2 - h a = h b$

Factor $a$ out of $- h a$ .

$a \cdot 2 + a (- h) = h b$

Factor $a$ out of $a \cdot 2 + a (- h)$ .

$a (2 - h) = h b$

Divide each term in $a (2 - h) = h b$ by $2 - h$ and simplify.

Divide each term in $a (2 - h) = h b$ by $2 - h$ .

$\frac{a (2 - h)}{2 - h} = \frac{h b}{2 - h}$

Simplify the left side.

Cancel the common factor of $2 - h$ .

Cancel the common factor.

$\frac{a (2 - h)}{2 - h} = \frac{h b}{2 - h}$

Divide $a$ by $1$ .

$a = \frac{h b}{2 - h}$