Solve for s q=r+rst for s

$q = r + r s t$ for $s$

Step 1

Rewrite the equation as $r + r s t = q$ .

$r + r s t = q$

Step 2

Subtract $r$ from both sides of the equation.

$r s t = q - r$

Step 3

Divide each term in $r s t = q - r$ by $r t$ and simplify.

Divide each term in $r s t = q - r$ by $r t$ .

$\frac{r s t}{r t} = \frac{q}{r t} + \frac{- r}{r t}$

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r s t}{r t} = \frac{q}{r t} + \frac{- r}{r t}$

Rewrite the expression.

$\frac{s t}{t} = \frac{q}{r t} + \frac{- r}{r t}$

Cancel the common factor of $t$ .

Cancel the common factor.

$\frac{s t}{t} = \frac{q}{r t} + \frac{- r}{r t}$

Divide $s$ by $1$ .

$s = \frac{q}{r t} + \frac{- r}{r t}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $r$ .

Cancel the common factor.

$s = \frac{q}{r t} + \frac{- r}{r t}$

Rewrite the expression.

$s = \frac{q}{r t} + \frac{- 1}{t}$

Move the negative in front of the fraction.

$s = \frac{q}{r t} - \frac{1}{t}$