Solve adiv(bdivc)=(ac)divb

$$a \div ( b \div c ) = ( a c ) \div b$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

$$b\neq 0\text{ and }c\neq 0$$

Solution Steps

Multiply both sides of the equation by b.

$$ca=ac$$

Subtract ac from both sides.

$$ca-ac=0$$

Combine ca and -ac to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for a

$$a\in \mathrm{R}$$

$$b\neq 0\text{ and }c\neq 0$$

Solution Steps

Multiply both sides of the equation by b.

$$ca=ac$$

Subtract ac from both sides.

$$ca-ac=0$$

Combine ca and -ac to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Solve for b

$$b\neq 0$$

$$c\neq 0$$

Solution Steps

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

$$ca=ac$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{R}$$

Variable b cannot be equal to 0.

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