Solve for r A=P+Prt for r

$A = P + P r t$ for $r$

Rewrite the equation as $P + P r t = A$ .

$P + P r t = A$

Subtract $P$ from both sides of the equation.

$P r t = A - P$

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.

$r = \frac{A}{P t} - \frac{1}{t}$