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

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

Solve for y (complex solution)

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

$$x\neq 0\text{ and }x\neq -i\text{ and }x\neq i$$

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 yx^{2}, the least common multiple of x^{2},y.

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

Combine all terms containing y.

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

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

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

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

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

Variable y cannot be equal to 0.

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

Solve for y

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

$$x\neq 0$$

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 yx^{2}, the least common multiple of x^{2},y.

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

Combine all terms containing y.

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

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

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

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

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

Variable y cannot be equal to 0.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\sqrt{-\frac{y}{y-1}}\text{, }y>0\text{ and }y<1$$