Solve 1*f(x)=1/x-5

$$1 \cdot f ( x ) = \frac { 1 } { x - 5 }$$

Solve for f

$$f=\frac{1}{x\left(x-5\right)}$$

$$x\neq 5\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-5.

$$1fx\left(x-5\right)=1$$

Use the distributive property to multiply 1fx by x-5.

$$fx^{2}-5fx=1$$

Combine all terms containing f.

$$\left(x^{2}-5x\right)f=1$$

Divide both sides by x^{2}-5x.

$$\frac{\left(x^{2}-5x\right)f}{x^{2}-5x}=\frac{1}{x^{2}-5x}$$

Dividing by x^{2}-5x undoes the multiplication by x^{2}-5x.

$$f=\frac{1}{x^{2}-5x}$$

Divide 1 by x^{2}-5x.

$$f=\frac{1}{x\left(x-5\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{25f^{2}+4f}}{2f}+\frac{5}{2}$$

$$x=-\frac{\sqrt{25f^{2}+4f}}{2f}+\frac{5}{2}\text{, }f\neq 0$$

Solve for x

$$x=\frac{\sqrt{25f^{2}+4f}}{2f}+\frac{5}{2}$$

$$x=-\frac{\sqrt{25f^{2}+4f}}{2f}+\frac{5}{2}\text{, }f>0\text{ or }f\leq -\frac{4}{25}$$