Solve for r a=p+prt

$a = p + p r t$

Step 1

Rewrite the equation as $p + p r t = a$ .

$p + p r t = a$

Step 2

Subtract $p$ from both sides of the equation.

$p r t = a - p$

Step 3

Divide each term in $p r t = a - p$ by $p t$ and simplify.

Divide each term in $p r t = a - p$ by $p t$ .

$\frac{p r t}{p t} = \frac{a}{p t} + \frac{- p}{p t}$

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{p r t}{p t} = \frac{a}{p t} + \frac{- p}{p t}$

Rewrite the expression.

$\frac{r t}{t} = \frac{a}{p t} + \frac{- p}{p t}$

Cancel the common factor of $t$ .

Cancel the common factor.

$\frac{r t}{t} = \frac{a}{p t} + \frac{- p}{p t}$

Divide $r$ by $1$ .

$r = \frac{a}{p t} + \frac{- p}{p t}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $p$ .

Cancel the common factor.

$r = \frac{a}{p t} + \frac{- p}{p t}$

Rewrite the expression.

$r = \frac{a}{p t} + \frac{- 1}{t}$

Move the negative in front of the fraction.

$r = \frac{a}{p t} - \frac{1}{t}$