Solve for s N=r(A-s)

$N = r (A - s)$

Rewrite the equation as $r (A - s) = N$ .

$r (A - s) = N$

Divide each term in $r (A - s) = N$ by $r$ and simplify.

Divide each term in $r (A - s) = N$ by $r$ .

$\frac{r (A - s)}{r} = \frac{N}{r}$

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r (A - s)}{r} = \frac{N}{r}$

Divide $A - s$ by $1$ .

$A - s = \frac{N}{r}$

Subtract $A$ from both sides of the equation.

$- s = \frac{N}{r} - A$

Divide each term in $- s = \frac{N}{r} - A$ by $- 1$ and simplify.

Divide each term in $- s = \frac{N}{r} - A$ by $- 1$ .

$\frac{- s}{- 1} = \frac{\frac{N}{r}}{- 1} + \frac{- A}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{s}{1} = \frac{\frac{N}{r}}{- 1} + \frac{- A}{- 1}$

Divide $s$ by $1$ .

$s = \frac{\frac{N}{r}}{- 1} + \frac{- A}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{N}{r}}{- 1}$ .

$s = - 1 \cdot \frac{N}{r} + \frac{- A}{- 1}$

Rewrite $- 1 \cdot \frac{N}{r}$ as $- \frac{N}{r}$ .

$s = - \frac{N}{r} + \frac{- A}{- 1}$

Dividing two negative values results in a positive value.

$s = - \frac{N}{r} + \frac{A}{1}$

Divide $A$ by $1$ .

$s = - \frac{N}{r} + A$