Solve x^2+1/y=1

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

Solve for y (complex solution)

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

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

Steps for Solving Linear Equation

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

$$yx^{2}+1=y$$

Subtract y from both sides.

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

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

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

Combine all terms containing y.

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

Divide both sides by x^{2}-1.

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

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

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

Variable y cannot be equal to 0.

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

Solve for y

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

$$|x|\neq 1$$

Steps for Solving Linear Equation

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

$$yx^{2}+1=y$$

Subtract y from both sides.

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

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

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

Combine all terms containing y.

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

Divide both sides by x^{2}-1.

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

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

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

Variable y cannot be equal to 0.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\sqrt{\frac{y-1}{y}}\text{, }y<0\text{ or }y\geq 1$$