Solve x-x/y=x^2*x^2/y

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

Solve for y (complex solution)

$$\left\{\begin{matrix}y=x^{3}+1\text{, }&x\neq -1\text{ and }x\neq \frac{-\sqrt{3}i+1}{2}\text{ and }x\neq \frac{1+\sqrt{3}i}{2}\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

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 y.

$$yx-x=x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$yx-x=x^{4}$$

Add x to both sides.

$$yx=x^{4}+x$$

The equation is in standard form.

$$xy=x^{4}+x$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{x^{4}+x}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{x^{4}+x}{x}$$

Divide x^{4}+x by x.

$$y=x^{3}+1$$

Variable y cannot be equal to 0.

$$y=x^{3}+1\text{, }y\neq 0$$

Solve for y

$$\left\{\begin{matrix}y=x^{3}+1\text{, }&x\neq -1\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

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 y.

$$yx-x=x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$yx-x=x^{4}$$

Add x to both sides.

$$yx=x^{4}+x$$

The equation is in standard form.

$$xy=x^{4}+x$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{x^{4}+x}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{x^{4}+x}{x}$$

Divide x^{4}+x by x.

$$y=x^{3}+1$$

Variable y cannot be equal to 0.

$$y=x^{3}+1\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=\sqrt[3]{y-1}$$

$$x=0$$

$$x=e^{\frac{2\pi i}{3}}\sqrt[3]{y-1}$$

$$x=e^{\frac{4\pi i}{3}}\sqrt[3]{y-1}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt[3]{y-1}$$

$$x=0\text{, }y\neq 0$$