Solve x+1/y-1=x/y-1

$$\frac{ x+1 }{ y-1 } = \frac{ x }{ y } -1$$

Solve for x

$$x=-y^{2}$$

$$y\neq 1\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y\left(y-1\right), the least common multiple of y-1,y.

$$y\left(x+1\right)=\left(y-1\right)x+y\left(y-1\right)\left(-1\right)$$

Use the distributive property to multiply y by x+1.

$$yx+y=\left(y-1\right)x+y\left(y-1\right)\left(-1\right)$$

Use the distributive property to multiply y-1 by x.

$$yx+y=yx-x+y\left(y-1\right)\left(-1\right)$$

Use the distributive property to multiply y by y-1.

$$yx+y=yx-x+\left(y^{2}-y\right)\left(-1\right)$$

Use the distributive property to multiply y^{2}-y by -1.

$$yx+y=yx-x-y^{2}+y$$

Subtract yx from both sides.

$$yx+y-yx=-x-y^{2}+y$$

Combine yx and -yx to get 0.

$$y=-x-y^{2}+y$$

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

$$-x-y^{2}+y=y$$

Add y^{2} to both sides.

$$-x+y=y+y^{2}$$

Subtract y from both sides.

$$-x=y+y^{2}-y$$

Combine y and -y to get 0.

$$-x=y^{2}$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{y^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{y^{2}}{-1}$$

Divide y^{2} by -1.

$$x=-y^{2}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=i\sqrt{x}\text{, }&x\neq 0\\y=-i\sqrt{x}\text{, }&x\neq -1\text{ and }x\neq 0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=-\sqrt{-x}\text{, }&x<0\\y=\sqrt{-x}\text{, }&x\neq -1\text{ and }x<0\end{matrix}\right.$$