Solve E=Ileft(R+V/nright)

$$E = I \left( R+ \frac{ V }{ n } \right)$$

Solve for I

$$\left\{\begin{matrix}I=\frac{En}{Rn+V}\text{, }&V\neq -Rn\text{ and }n\neq 0\\I\in \mathrm{R}\text{, }&E=0\text{ and }V=-Rn\text{ and }n\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n.

$$En=I\left(R+\frac{V}{n}\right)n$$

To add or subtract expressions, expand them to make their denominators the same. Multiply R times \frac{n}{n}.

$$En=I\left(\frac{Rn}{n}+\frac{V}{n}\right)n$$

Since \frac{Rn}{n} and \frac{V}{n} have the same denominator, add them by adding their numerators.

$$En=I\times \frac{Rn+V}{n}n$$

Express I\times \frac{Rn+V}{n} as a single fraction.

$$En=\frac{I\left(Rn+V\right)}{n}n$$

Express \frac{I\left(Rn+V\right)}{n}n as a single fraction.

$$En=\frac{I\left(Rn+V\right)n}{n}$$

Cancel out n in both numerator and denominator.

$$En=I\left(Rn+V\right)$$

Use the distributive property to multiply I by Rn+V.

$$En=IRn+IV$$

Swap sides so that all variable terms are on the left hand side.

$$IRn+IV=En$$

Combine all terms containing I.

$$\left(Rn+V\right)I=En$$

Divide both sides by V+Rn.

$$\frac{\left(Rn+V\right)I}{Rn+V}=\frac{En}{Rn+V}$$

Dividing by V+Rn undoes the multiplication by V+Rn.

$$I=\frac{En}{Rn+V}$$

Solve for E

$$E=\frac{I\left(Rn+V\right)}{n}$$

$$n\neq 0$$