Solve y^2/x=1/x-1

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

Solve for x (complex solution)

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

$$y\neq 0\text{ and }y\neq -1\text{ and }y\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right), the least common multiple of x,x-1.

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

Use the distributive property to multiply x-1 by y^{2}.

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

Subtract x from both sides.

$$xy^{2}-y^{2}-x=0$$

Add y^{2} to both sides. Anything plus zero gives itself.

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

Combine all terms containing x.

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

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

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

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

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

Variable x cannot be equal to any of the values 1,0.

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

Solve for x

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

$$y\neq 0\text{ and }|y|\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right), the least common multiple of x,x-1.

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

Use the distributive property to multiply x-1 by y^{2}.

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

Subtract x from both sides.

$$xy^{2}-y^{2}-x=0$$

Add y^{2} to both sides. Anything plus zero gives itself.

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

Combine all terms containing x.

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

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

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

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

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

Variable x cannot be equal to any of the values 1,0.

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

Solve for y (complex solution)

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

$$y=\left(x-1\right)^{-\frac{1}{2}}\sqrt{x}\text{, }x\neq 0\text{ and }x\neq 1$$

Solve for y

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

$$y=-\sqrt{\frac{x}{x-1}}\text{, }x<0\text{ or }x>1$$