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

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

$$1=yx^{2}-2yx+y$$

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

$$yx^{2}-2yx+y=1$$

Combine all terms containing y.

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

Divide both sides by x^{2}-2x+1.

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

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

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

Divide 1 by x^{2}-2x+1.

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

Solve for x (complex solution)

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

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

Solve for x

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

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