Solve AB/BC=AK/KC

$$\frac { A B } { B C } = \frac { A K } { K C }$$

Solve for A

$$A\in \mathrm{R}$$

$$B\neq 0\text{ and }C\neq 0\text{ and }K\neq 0$$

Solution Steps

Multiply both sides of the equation by BCK, the least common multiple of BC,KC.

$$KAB=BAK$$

Subtract BAK from both sides.

$$KAB-BAK=0$$

Combine KAB and -BAK to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any A.

$$A\in \mathrm{R}$$

Solve for B

$$B\neq 0$$

$$K\neq 0\text{ and }C\neq 0$$

Solution Steps

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by BCK, the least common multiple of BC,KC.

$$KAB=BAK$$

Subtract BAK from both sides.

$$KAB-BAK=0$$

Combine KAB and -BAK to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any B.

$$B\in \mathrm{R}$$

Variable B cannot be equal to 0.

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