Solve in Terms of the Arbitrary Variable h v=1/3Bh

$v = \frac{1}{3} B h$

Step 1

Multiply $\frac{1}{3} (B h)$ .

Combine $B$ and $\frac{1}{3}$ .

$v = \frac{B}{3} h$

Combine $\frac{B}{3}$ and $h$ .

$v = \frac{B h}{3}$

Step 2

Solve the equation for $B$ .

Multiply both sides by $3$ .

$\frac{B h}{3} \cdot 3 = \frac{1}{3} \cdot (B h) \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{B h}{3} \cdot 3 = \frac{1}{3} \cdot (B h) \cdot 3$

Rewrite the expression.

$B h = \frac{1}{3} \cdot (B h) \cdot 3$

Simplify the right side.

Simplify $\frac{1}{3} \cdot (B h) \cdot 3$ .

Multiply $\frac{1}{3} (B h)$ .

Combine $B$ and $\frac{1}{3}$ .

$B h = \frac{B}{3} h \cdot 3$

Combine $\frac{B}{3}$ and $h$ .

$B h = \frac{B h}{3} \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$B h = \frac{B h}{3} \cdot 3$

Rewrite the expression.

$B h = B h$

Solve for $B$ .

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

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

$B h - B h = 0$

Subtract $B h$ from $B h$ .

$0 = 0$

Since $0 = 0$ , the equation will always be true.

Always true