Solve for n i=(na)/(nr+R)

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

Step 1

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

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

Step 2

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.

$n r + R, 1$

Remove parentheses.

$n r + R, 1$

The LCM of one and any expression is the expression.

$n r + R$

Step 3

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

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

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

Simplify the left side.

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Apply the distributive property.

$n a = i n r + i R$

Step 4

Solve the equation.

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

$n a - i n r = i R$

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

Factor $n$ out of $n a$ .

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

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

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

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

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

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

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

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

Simplify the left side.

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

Cancel the common factor.

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

Divide $n$ by $1$ .

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