Solve xy^2=x-8

$$x y ^ { 2 } = x - 8$$

Solve for x (complex solution)

$$x=-\frac{8}{y^{2}-1}$$

$$y\neq -1\text{ and }y\neq 1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$xy^{2}-x=-8$$

Combine all terms containing x.

$$\left(y^{2}-1\right)x=-8$$

Divide both sides by y^{2}-1.

$$\frac{\left(y^{2}-1\right)x}{y^{2}-1}=-\frac{8}{y^{2}-1}$$

Dividing by y^{2}-1 undoes the multiplication by y^{2}-1.

$$x=-\frac{8}{y^{2}-1}$$

Solve for x

$$x=-\frac{8}{y^{2}-1}$$

$$|y|\neq 1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$xy^{2}-x=-8$$

Combine all terms containing x.

$$\left(y^{2}-1\right)x=-8$$

Divide both sides by y^{2}-1.

$$\frac{\left(y^{2}-1\right)x}{y^{2}-1}=-\frac{8}{y^{2}-1}$$

Dividing by y^{2}-1 undoes the multiplication by y^{2}-1.

$$x=-\frac{8}{y^{2}-1}$$

Solve for y (complex solution)

$$y=-\sqrt{\frac{x-8}{x}}$$

$$y=\sqrt{\frac{x-8}{x}}\text{, }x\neq 0$$

Solve for y

$$y=\sqrt{\frac{x-8}{x}}$$

$$y=-\sqrt{\frac{x-8}{x}}\text{, }x\geq 8\text{ or }x<0$$