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

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

Step 1

Rewrite the equation as $\frac{h}{2} \cdot (a + b) = s$ .

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

Step 2

Multiply each term in $\frac{h}{2} \cdot (a + b) = s$ by $\frac{2}{h}$ to eliminate the fractions.

Multiply each term in $\frac{h}{2} \cdot (a + b) = s$ by $\frac{2}{h}$ .

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

Simplify the left side.

Simplify terms.

Apply the distributive property.

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

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

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

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

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

Multiply $\frac{h a}{2} + \frac{h b}{2}$ by $\frac{2}{h}$ .

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

Simplify the numerator.

Combine the numerators over the common denominator.

$\frac{\frac{h a + h b}{2} \cdot 2}{h} = s \frac{2}{h}$

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

Factor $h$ out of $h a$ .

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

Factor $h$ out of $h b$ .

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

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

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

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

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

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{h (a + b) \cdot 2}{2}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{\frac{h (a + b)}{1}}{h} = s \frac{2}{h}$

Divide $h (a + b)$ by $1$ .

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

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $a + b$ by $1$ .

$a + b = s \frac{2}{h}$

Simplify the right side.

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

$a + b = \frac{s \cdot 2}{h}$

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

$a + b = \frac{2 s}{h}$

Step 3

Subtract $a$ from both sides of the equation.

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

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

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