Solve p^-1=1/p

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

Solve for p

$$p\neq 0$$

Solution Steps

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

$$pp^{-1}=1$$

Subtract 1 from both sides.

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

Reorder the terms.

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

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

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

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

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any p.

$$p\in \mathrm{R}$$

Variable p cannot be equal to 0.

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