Solve for n i=(pn)/(rn+a)

$i = \frac{p n}{r n + a}$

Rewrite the equation as $\frac{p n}{r n + a} = i$ .

$\frac{p n}{r n + a} = i$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$r n + a, 1$

Remove parentheses.

$r n + a, 1$

The LCM of one and any expression is the expression.

$r n + a$

Multiply each term in $\frac{p n}{r n + a} = i$ by $r n + a$ to eliminate the fractions.

Multiply each term in $\frac{p n}{r n + a} = i$ by $r n + a$ .

$\frac{p n}{r n + a} (r n + a) = i (r n + a)$

Simplify the left side.

Cancel the common factor of $r n + a$ .

Cancel the common factor.

$\frac{p n}{r n + a} (r n + a) = i (r n + a)$

Rewrite the expression.

$p n = i (r n + a)$

Simplify the right side.

Apply the distributive property.

$p n = i r n + i a$

Solve the equation.

Subtract $i r n$ from both sides of the equation.

$p n - i r n = i a$

Factor $n$ out of $p n - i r n$ .

Factor $n$ out of $p n$ .

$n p - i r n = i a$

Factor $n$ out of $- i r n$ .

$n p + n (- i r) = i a$

Factor $n$ out of $n p + n (- i r)$ .

$n (p - i r) = i a$

Divide each term in $n (p - i r) = i a$ by $p - i r$ and simplify.

Divide each term in $n (p - i r) = i a$ by $p - i r$ .

$\frac{n (p - i r)}{p - i r} = \frac{i a}{p - i r}$

Simplify the left side.

Cancel the common factor of $p - i r$ .

Cancel the common factor.

$\frac{n (p - i r)}{p - i r} = \frac{i a}{p - i r}$

Divide $n$ by $1$ .

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