Solve for a R^3=5+H/a

$R^{3} = 5 + \frac{H}{a}$

Step 1

Rewrite the equation as $5 + \frac{H}{a} = R^{3}$ .

$5 + \frac{H}{a} = R^{3}$

Step 2

Subtract $5$ from both sides of the equation.

$\frac{H}{a} = R^{3} - 5$

Step 3

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.

$a, 1, 1$

The LCM of one and any expression is the expression.

$a$

Step 4

Multiply each term in $\frac{H}{a} = R^{3} - 5$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{H}{a} = R^{3} - 5$ by $a$ .

$\frac{H}{a} a = R^{3} a - 5 a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{H}{a} a = R^{3} a - 5 a$

Rewrite the expression.

$H = R^{3} a - 5 a$

Step 5

Solve the equation.

Rewrite the equation as $R^{3} a - 5 a = H$ .

$R^{3} a - 5 a = H$

Factor $a$ out of $R^{3} a - 5 a$ .

Factor $a$ out of $R^{3} a$ .

$a R^{3} - 5 a = H$

Factor $a$ out of $- 5 a$ .

$a R^{3} + a \cdot - 5 = H$

Factor $a$ out of $a R^{3} + a \cdot - 5$ .

$a (R^{3} - 5) = H$

Divide each term in $a (R^{3} - 5) = H$ by $R^{3} - 5$ and simplify.

Divide each term in $a (R^{3} - 5) = H$ by $R^{3} - 5$ .

$\frac{a (R^{3} - 5)}{R^{3} - 5} = \frac{H}{R^{3} - 5}$

Simplify the left side.

Cancel the common factor of $R^{3} - 5$ .

Cancel the common factor.

$\frac{a (R^{3} - 5)}{R^{3} - 5} = \frac{H}{R^{3} - 5}$

Divide $a$ by $1$ .

$a = \frac{H}{R^{3} - 5}$