Solve a^2/b=a^3/ab

$$\frac { a ^ { 2 } } { b } = \frac { a ^ { 3 } } { a b }$$

Solve for a

$$a\neq 0$$

$$b\neq 0$$

Solution Steps

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of b,ab.

$$aa^{2}=a^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$a^{3}=a^{3}$$

Subtract a^{3} from both sides.

$$a^{3}-a^{3}=0$$

Combine a^{3} and -a^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

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

Variable a cannot be equal to 0.

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

Solve for b

$$b\neq 0$$

$$a\neq 0$$

Solution Steps

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

$$aa^{2}=a^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$a^{3}=a^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

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

Variable b cannot be equal to 0.

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