Solve varepsilon-x=(I-x)f/varepsilon

$$\varepsilon - x = ( I - x ) \frac { f } { \varepsilon }$$

Solve for I (complex solution)

$$\left\{\begin{matrix}I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}\text{, }&f\neq 0\text{ and }\epsilon \neq 0\\I\in \mathrm{C}\text{, }&\epsilon =x\text{ and }f=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Multiply \epsilon and \epsilon to get \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Use the distributive property to multiply I-x by f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

Add xf to both sides.

$$If=\epsilon ^{2}-x\epsilon +xf$$

The equation is in standard form.

$$fI=fx-x\epsilon +\epsilon ^{2}$$

Divide both sides by f.

$$\frac{fI}{f}=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

Dividing by f undoes the multiplication by f.

$$I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}\text{, }&x\neq I\text{ and }\epsilon \neq 0\\f\in \mathrm{C}\text{, }&\epsilon =I\text{ and }x=I\text{ and }I\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Multiply \epsilon and \epsilon to get \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Use the distributive property to multiply I-x by f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

Combine all terms containing f.

$$\left(I-x\right)f=\epsilon ^{2}-x\epsilon$$

Divide both sides by I-x.

$$\frac{\left(I-x\right)f}{I-x}=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$

Dividing by I-x undoes the multiplication by I-x.

$$f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$

Solve for I

$$\left\{\begin{matrix}I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}\text{, }&f\neq 0\text{ and }\epsilon \neq 0\\I\in \mathrm{R}\text{, }&\epsilon =x\text{ and }f=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Multiply \epsilon and \epsilon to get \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Use the distributive property to multiply I-x by f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

Add xf to both sides.

$$If=\epsilon ^{2}-x\epsilon +xf$$

The equation is in standard form.

$$fI=fx-x\epsilon +\epsilon ^{2}$$

Divide both sides by f.

$$\frac{fI}{f}=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

Dividing by f undoes the multiplication by f.

$$I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}\text{, }&x\neq I\text{ and }\epsilon \neq 0\\f\in \mathrm{R}\text{, }&\epsilon =I\text{ and }x=I\text{ and }I\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Multiply \epsilon and \epsilon to get \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Use the distributive property to multiply I-x by f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

Combine all terms containing f.

$$\left(I-x\right)f=\epsilon ^{2}-x\epsilon$$

Divide both sides by I-x.

$$\frac{\left(I-x\right)f}{I-x}=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$

Dividing by I-x undoes the multiplication by I-x.

$$f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$