Solve xy-y-1-x^2=0

$$x y - y - 1 - x ^ { 2 } = 0$$

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Add 1 to both sides. Anything plus zero gives itself.

$$xy-y-x^{2}=1$$

Add x^{2} to both sides.

$$xy-y=1+x^{2}$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x-1.

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

Dividing by x-1 undoes the multiplication by x-1.

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

Solve for x (complex solution)

$$x=\frac{-\sqrt{y^{2}-4y-4}+y}{2}$$

$$x=\frac{\sqrt{y^{2}-4y-4}+y}{2}$$

Solve for x

$$x=\frac{-\sqrt{y^{2}-4y-4}+y}{2}$$

$$x=\frac{\sqrt{y^{2}-4y-4}+y}{2}\text{, }y\geq 2\sqrt{2}+2\text{ or }y\leq 2-2\sqrt{2}$$