Solve for a h^3+g/a=m

$h^{3} + \frac{g}{a} = m$

Step 1

Subtract $h^{3}$ from both sides of the equation.

$\frac{g}{a} = m - h^{3}$

Step 2

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 3

Multiply each term in $\frac{g}{a} = m - h^{3}$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{g}{a} = m - h^{3}$ by $a$ .

$\frac{g}{a} a = m a - h^{3} a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{g}{a} a = m a - h^{3} a$

Rewrite the expression.

$g = m a - h^{3} a$

Step 4

Solve the equation.

Rewrite the equation as $m a - h^{3} a = g$ .

$m a - h^{3} a = g$

Factor $a$ out of $m a - h^{3} a$ .

Factor $a$ out of $m a$ .

$a m - h^{3} a = g$

Factor $a$ out of $- h^{3} a$ .

$a m + a (- h^{3}) = g$

Factor $a$ out of $a m + a (- h^{3})$ .

$a (m - h^{3}) = g$

Divide each term in $a (m - h^{3}) = g$ by $m - h^{3}$ and simplify.

Divide each term in $a (m - h^{3}) = g$ by $m - h^{3}$ .

$\frac{a (m - h^{3})}{m - h^{3}} = \frac{g}{m - h^{3}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{a (m - h^{3})}{m - h^{3}} = \frac{g}{m - h^{3}}$

Divide $a$ by $1$ .

$a = \frac{g}{m - h^{3}}$