Solve y=y-1/x^2-1

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

Solve for y (complex solution)

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

$$x\neq -\sqrt{2}\text{ and }x\neq \sqrt{2}\text{ and }x\neq -1\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Subtract \frac{y-1}{x^{2}-1} from both sides.

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

Factor x^{2}-1.

$$y-\frac{y-1}{\left(x-1\right)\left(x+1\right)}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.

$$\frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{y-1}{\left(x-1\right)\left(x+1\right)}=0$$

Since \frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{y-1}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y\left(x-1\right)\left(x+1\right)-\left(y-1\right)}{\left(x-1\right)\left(x+1\right)}=0$$

Do the multiplications in y\left(x-1\right)\left(x+1\right)-\left(y-1\right).

$$\frac{x^{2}y+yx-yx-y-y+1}{\left(x-1\right)\left(x+1\right)}=0$$

Combine like terms in x^{2}y+yx-yx-y-y+1.

$$\frac{x^{2}y+1-2y}{\left(x-1\right)\left(x+1\right)}=0$$

Multiply both sides of the equation by \left(x-1\right)\left(x+1\right).

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

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing y.

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

Divide both sides by x^{2}-2.

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

Dividing by x^{2}-2 undoes the multiplication by x^{2}-2.

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

Solve for y

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

$$|x|\neq \sqrt{2}\text{ and }|x|\neq 1$$

Steps for Solving Linear Equation

Subtract \frac{y-1}{x^{2}-1} from both sides.

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

Factor x^{2}-1.

$$y-\frac{y-1}{\left(x-1\right)\left(x+1\right)}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.

$$\frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{y-1}{\left(x-1\right)\left(x+1\right)}=0$$

Since \frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{y-1}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y\left(x-1\right)\left(x+1\right)-\left(y-1\right)}{\left(x-1\right)\left(x+1\right)}=0$$

Do the multiplications in y\left(x-1\right)\left(x+1\right)-\left(y-1\right).

$$\frac{x^{2}y+yx-yx-y-y+1}{\left(x-1\right)\left(x+1\right)}=0$$

Combine like terms in x^{2}y+yx-yx-y-y+1.

$$\frac{x^{2}y+1-2y}{\left(x-1\right)\left(x+1\right)}=0$$

Multiply both sides of the equation by \left(x-1\right)\left(x+1\right).

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

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing y.

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

Divide both sides by x^{2}-2.

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

Dividing by x^{2}-2 undoes the multiplication by x^{2}-2.

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

Solve for x (complex solution)

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

$$x=\sqrt{2-\frac{1}{y}}\text{, }y\neq 1\text{ and }y\neq 0$$

Solve for x

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

$$x=-\sqrt{2-\frac{1}{y}}\text{, }y<0\text{ or }\left(y\neq 1\text{ and }y\geq \frac{1}{2}\right)$$