Solve xt-x^2-1/x^2=0

$$\frac{ xt- { x }^{ 2 } -1 }{ { x }^{ 2 } } =0$$

Solve for t

$$t=x+\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

$$xt-x^{2}-1=0$$

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

$$xt-1=x^{2}$$

Add 1 to both sides.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide x^{2}+1 by x.

$$t=x+\frac{1}{x}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{t^{2}-4}+t}{2}$$

$$x=\frac{\sqrt{t^{2}-4}+t}{2}$$

Solve for x

$$x=\frac{-\sqrt{t^{2}-4}+t}{2}$$

$$x=\frac{\sqrt{t^{2}-4}+t}{2}\text{, }|t|\geq 2$$