Solve x/w=z/y^2

$$\frac { x } { w } = \frac { z } { y ^ { 2 } }$$

Solve for w

$$\left\{\begin{matrix}w=\frac{xy^{2}}{z}\text{, }&y\neq 0\text{ and }x\neq 0\text{ and }z\neq 0\\w\neq 0\text{, }&z=0\text{ and }x=0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable w cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by wy^{2}, the least common multiple of w,y^{2}.

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

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

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

The equation is in standard form.

$$zw=xy^{2}$$

Divide both sides by z.

$$\frac{zw}{z}=\frac{xy^{2}}{z}$$

Dividing by z undoes the multiplication by z.

$$w=\frac{xy^{2}}{z}$$

Variable w cannot be equal to 0.

$$w=\frac{xy^{2}}{z}\text{, }w\neq 0$$

Solve for x

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

$$w\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by wy^{2}, the least common multiple of w,y^{2}.

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

Divide both sides by y^{2}.

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

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

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