Solve e^x-y/x-1=0

$${ e }^{ x } - \frac{ y }{ x-1 } = 0$$

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

$$\left(x-1\right)e^{x}-y=0$$

Use the distributive property to multiply x-1 by e^{x}.

$$xe^{x}-e^{x}-y=0$$

Subtract xe^{x} from both sides. Anything subtracted from zero gives its negation.

$$-e^{x}-y=-xe^{x}$$

Add e^{x} to both sides.

$$-y=-xe^{x}+e^{x}$$

The equation is in standard form.

$$-y=e^{x}-xe^{x}$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide \left(1-x\right)e^{x} by -1.

$$y=xe^{x}-e^{x}$$