Solve for r A=p(1+nr) for r

$A = p (1 + n r)$ for $r$

Step 1

Rewrite the equation as $p (1 + n r) = A$ .

$p (1 + n r) = A$

Step 2

Divide each term in $p (1 + n r) = A$ by $p$ and simplify.

Divide each term in $p (1 + n r) = A$ by $p$ .

$\frac{p (1 + n r)}{p} = \frac{A}{p}$

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{p (1 + n r)}{p} = \frac{A}{p}$

Divide $1 + n r$ by $1$ .

$1 + n r = \frac{A}{p}$

Step 3

Subtract $1$ from both sides of the equation.

$n r = \frac{A}{p} - 1$

Step 4

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

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

$\frac{n r}{n} = \frac{\frac{A}{p}}{n} + \frac{- 1}{n}$

Simplify the left side.

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{n r}{n} = \frac{\frac{A}{p}}{n} + \frac{- 1}{n}$

Divide $r$ by $1$ .

$r = \frac{\frac{A}{p}}{n} + \frac{- 1}{n}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$r = \frac{A}{p} \cdot \frac{1}{n} + \frac{- 1}{n}$

Multiply $\frac{A}{p}$ by $\frac{1}{n}$ .

$r = \frac{A}{p n} + \frac{- 1}{n}$

Move the negative in front of the fraction.

$r = \frac{A}{p n} - \frac{1}{n}$