Solve y=e^y/x-1

$$y = \frac { e ^ { y } } { x } - 1$$

Solve for x

$$x=\frac{e^{y}}{y+1}$$

$$y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$yx=e^{y}+x\left(-1\right)$$

Subtract x\left(-1\right) from both sides.

$$yx-x\left(-1\right)=e^{y}$$

Multiply -1 and -1 to get 1.

$$yx+x=e^{y}$$

Combine all terms containing x.

$$\left(y+1\right)x=e^{y}$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{e^{y}}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

$$x=\frac{e^{y}}{y+1}$$

Variable x cannot be equal to 0.

$$x=\frac{e^{y}}{y+1}\text{, }x\neq 0$$