Solve ac/b=c/b*a

$$a \frac { c } { b } = \frac { c } { b } \times a$$

Solve for a

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

$$b\neq 0$$

Solution Steps

Multiply both sides of the equation by b.

$$ac=ca$$

Subtract ca from both sides.

$$ac-ca=0$$

Combine ac and -ca to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

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

Solve for b

$$b\neq 0$$

Solution Steps

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

$$ac=ca$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

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

Variable b cannot be equal to 0.

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