Solve for g A=((f+g)/2)h

$A = (\frac{f + g}{2}) h$

Step 1

Rewrite the equation as $\frac{f + g}{2} \cdot h = A$ .

$\frac{f + g}{2} \cdot h = A$

Step 2

Combine $\frac{f + g}{2}$ and $h$ .

$\frac{(f + g) h}{2} = A$

Step 3

Divide each term in $\frac{(f + g) h}{2} = A$ by $h$ and simplify.

Divide each term in $\frac{(f + g) h}{2} = A$ by $h$ .

$\frac{\frac{(f + g) h}{2}}{h} = \frac{A}{h}$

Simplify the left side.

Multiply the numerator by the reciprocal of the denominator.

$\frac{(f + g) h}{2} \cdot \frac{1}{h} = \frac{A}{h}$

Cancel the common factor of $h$ .

Factor $h$ out of $(f + g) h$ .

$\frac{h (f + g)}{2} \cdot \frac{1}{h} = \frac{A}{h}$

Cancel the common factor.

$\frac{h (f + g)}{2} \cdot \frac{1}{h} = \frac{A}{h}$

Rewrite the expression.

$\frac{f + g}{2} = \frac{A}{h}$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{f + g}{2} = 2 \frac{A}{h}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{f + g}{2} = 2 \frac{A}{h}$

Rewrite the expression.

$f + g = 2 \frac{A}{h}$

Simplify the right side.

Combine $2$ and $\frac{A}{h}$ .

$f + g = \frac{2 A}{h}$

Step 6

Subtract $f$ from both sides of the equation.

$g = \frac{2 A}{h} - f$