Solve frac{sqrt{x^2-2}}{ydiv3z}=5z

$$\frac{ \sqrt{ { x }^{ 2 } -2 } }{ y \div 3z } =5z$$

Solve for y (complex solution)

$$y=\frac{3\sqrt{x^{2}-2}}{5z^{2}}$$

$$x\neq -\sqrt{2}\text{ and }x\neq \sqrt{2}\text{ and }z\neq 0$$

Steps for Solving Linear Equation

Express \frac{y}{3}z as a single fraction.

$$\frac{\sqrt{x^{2}-2}}{\frac{yz}{3}}=5z$$

Divide \sqrt{x^{2}-2} by \frac{yz}{3} by multiplying \sqrt{x^{2}-2} by the reciprocal of \frac{yz}{3}.

$$\frac{\sqrt{x^{2}-2}\times 3}{yz}=5z$$

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

$$\sqrt{x^{2}-2}\times 3=5zyz$$

Reorder the terms.

$$3\sqrt{x^{2}-2}=5yzz$$

Multiply z and z to get z^{2}.

$$3\sqrt{x^{2}-2}=5yz^{2}$$

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

$$5yz^{2}=3\sqrt{x^{2}-2}$$

The equation is in standard form.

$$5z^{2}y=3\sqrt{x^{2}-2}$$

Divide both sides by 5z^{2}.

$$\frac{5z^{2}y}{5z^{2}}=\frac{3\sqrt{x^{2}-2}}{5z^{2}}$$

Dividing by 5z^{2} undoes the multiplication by 5z^{2}.

$$y=\frac{3\sqrt{x^{2}-2}}{5z^{2}}$$

Variable y cannot be equal to 0.

$$y=\frac{3\sqrt{x^{2}-2}}{5z^{2}}\text{, }y\neq 0$$

Solve for y

$$y=\frac{3\sqrt{x^{2}-2}}{5z^{2}}$$

$$z\neq 0\text{ and }|x|>\sqrt{2}$$

Steps for Solving Linear Equation

Express \frac{y}{3}z as a single fraction.

$$\frac{\sqrt{x^{2}-2}}{\frac{yz}{3}}=5z$$

Divide \sqrt{x^{2}-2} by \frac{yz}{3} by multiplying \sqrt{x^{2}-2} by the reciprocal of \frac{yz}{3}.

$$\frac{\sqrt{x^{2}-2}\times 3}{yz}=5z$$

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

$$\sqrt{x^{2}-2}\times 3=5zyz$$

Reorder the terms.

$$3\sqrt{x^{2}-2}=5yzz$$

Multiply z and z to get z^{2}.

$$3\sqrt{x^{2}-2}=5yz^{2}$$

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

$$5yz^{2}=3\sqrt{x^{2}-2}$$

The equation is in standard form.

$$5z^{2}y=3\sqrt{x^{2}-2}$$

Divide both sides by 5z^{2}.

$$\frac{5z^{2}y}{5z^{2}}=\frac{3\sqrt{x^{2}-2}}{5z^{2}}$$

Dividing by 5z^{2} undoes the multiplication by 5z^{2}.

$$y=\frac{3\sqrt{x^{2}-2}}{5z^{2}}$$

Variable y cannot be equal to 0.

$$y=\frac{3\sqrt{x^{2}-2}}{5z^{2}}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{25y^{2}z^{4}+18}}{3}$$

$$x=\frac{\sqrt{25y^{2}z^{4}+18}}{3}\text{, }arg(yz^{2})<\pi \text{ and }z\neq 0\text{ and }y\neq 0$$

Solve for x

$$x=-\frac{\sqrt{25y^{2}z^{4}+18}}{3}$$

$$x=\frac{\sqrt{25y^{2}z^{4}+18}}{3}\text{, }z\neq 0\text{ and }y>0$$