Solve fx=1/x-1

$$fx = \frac{ 1 }{ x-1 }$$

Solve for f

$$f=\frac{1}{x\left(x-1\right)}$$

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

$$fx\left(x-1\right)=1$$

Use the distributive property to multiply fx by x-1.

$$fx^{2}-fx=1$$

Combine all terms containing f.

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

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

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

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

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

Divide 1 by x^{2}-x.

$$f=\frac{1}{x\left(x-1\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{f\left(f+4\right)}+f}{2f}$$

$$x=\frac{-\sqrt{f\left(f+4\right)}+f}{2f}\text{, }f\neq 0$$

Solve for x

$$x=\frac{\sqrt{f\left(f+4\right)}+f}{2f}$$

$$x=\frac{-\sqrt{f\left(f+4\right)}+f}{2f}\text{, }f>0\text{ or }f\leq -4$$