Solve f(x)=x+1/x,f

$$f ( x ) = x + 1 / x , f$$

Solve for f

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$fxx=xx+1$$

Multiply x and x to get x^{2}.

$$fx^{2}=xx+1$$

Multiply x and x to get x^{2}.

$$fx^{2}=x^{2}+1$$

The equation is in standard form.

$$x^{2}f=x^{2}+1$$

Divide both sides by x^{2}.

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

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

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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