Solve x^-1=1/x

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

Solve for x

$$x\neq 0$$

Solution Steps

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$xx^{-1}=1$$

Subtract 1 from both sides.

$$xx^{-1}-1=0$$

Reorder the terms.

$$-1+\frac{1}{x}x=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\left(-1\right)+1x=0$$

Combine x\left(-1\right) and 1x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to 0.

$$x\in \mathrm{R}\setminus 0$$