Solve y^2=x^-1

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

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

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

Reorder the terms.

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

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

$$1=xy^{2}$$

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

$$xy^{2}=1$$

The equation is in standard form.

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

Divide both sides by y^{2}.

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

Dividing by y^{2} undoes the multiplication by y^{2}.

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

Variable x cannot be equal to 0.

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

Solve for y (complex solution)

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

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

Solve for y

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

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