Solve 1/x=sqrt{y}

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

Solve for x (complex solution)

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

$$y\neq 0$$

Steps for Solving Linear Equation

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

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

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

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

The equation is in standard form.

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

Divide both sides by \sqrt{y}.

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

Dividing by \sqrt{y} undoes the multiplication by \sqrt{y}.

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

Divide 1 by \sqrt{y}.

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

Variable x cannot be equal to 0.

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

Solve for x

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

$$y>0$$

Steps for Solving Linear Equation

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

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

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

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

The equation is in standard form.

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

Divide both sides by \sqrt{y}.

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

Dividing by \sqrt{y} undoes the multiplication by \sqrt{y}.

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

Variable x cannot be equal to 0.

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

Solve for y

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

$$x>0$$

Steps for Solving Radical Equations

Multiply both sides of the equation by x.

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

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

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Square both sides of the equation.

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

Solve for y (complex solution)

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

$$arg(\sqrt{\frac{1}{x^{2}}}x)<\pi \text{ and }x\neq 0$$