Solve for B r^3=f/B+h

$r^{3} = \frac{f}{B} + h$

Rewrite the equation as $\frac{f}{B} + h = r^{3}$ .

$\frac{f}{B} + h = r^{3}$

Subtract $h$ from both sides of the equation.

$\frac{f}{B} = r^{3} - h$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$B, 1, 1$

The LCM of one and any expression is the expression.

$B$

Multiply each term in $\frac{f}{B} = r^{3} - h$ by $B$ to eliminate the fractions.

Multiply each term in $\frac{f}{B} = r^{3} - h$ by $B$ .

$\frac{f}{B} B = r^{3} B - h B$

Simplify the left side.

Cancel the common factor of $B$ .

Cancel the common factor.

$\frac{f}{B} B = r^{3} B - h B$

Rewrite the expression.

$f = r^{3} B - h B$

Solve the equation.

Rewrite the equation as $r^{3} B - h B = f$ .

$r^{3} B - h B = f$

Factor $B$ out of $r^{3} B - h B$ .

Factor $B$ out of $r^{3} B$ .

$B r^{3} - h B = f$

Factor $B$ out of $- h B$ .

$B r^{3} + B (- h) = f$

Factor $B$ out of $B r^{3} + B (- h)$ .

$B (r^{3} - h) = f$

Divide each term in $B (r^{3} - h) = f$ by $r^{3} - h$ and simplify.

Divide each term in $B (r^{3} - h) = f$ by $r^{3} - h$ .

$\frac{B (r^{3} - h)}{r^{3} - h} = \frac{f}{r^{3} - h}$

Simplify the left side.

Cancel the common factor of $r^{3} - h$ .

Cancel the common factor.

$\frac{B (r^{3} - h)}{r^{3} - h} = \frac{f}{r^{3} - h}$

Divide $B$ by $1$ .

$B = \frac{f}{r^{3} - h}$