Solve for n a=p(1+nr) for n

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

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 $r$ and simplify.

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

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

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $\frac{a}{p}$ by $\frac{1}{r}$ .

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

Move the negative in front of the fraction.

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