# How do you solve for n in  I = (nE)/(nr+R)?

Apr 27, 2016

$n = \frac{R I}{E - r I}$

#### Explanation:

Given:

$I = \frac{n E}{n r + R}$

Transpose and multiply both sides by $\left(n r + R\right)$ to get:

$n E = \left(n r + R\right) I = n r I + R I$

Transpose and subtract $n r I$ from both sides to get:

$R I = n E - n r I = n \left(E - r I\right)$

Transpose and divide both sides by $\left(E - r I\right)$ to get:

$n = \frac{R I}{E - r I}$