Solve 3/x*1/g=3/xg

$$\frac { 3 } { x } \cdot \frac { 1 } { g } = \frac { 3 } { x g }$$

Solve for g

$$g\neq 0$$

$$x\neq 0$$

Solution Steps

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

$$g\times 3\times \frac{1}{g}=3$$

Express g\times \frac{1}{g} as a single fraction.

$$\frac{g}{g}\times 3=3$$

Express \frac{g}{g}\times 3 as a single fraction.

$$\frac{g\times 3}{g}=3$$

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

$$g\times 3=3g$$

Reorder the terms.

$$\text{true}$$

This is true for any g.

$$g\in \mathrm{R}$$

Variable g cannot be equal to 0.

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

Solve for x

$$x\neq 0$$

$$g\neq 0$$

Solution Steps

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

$$g\times 3\times \frac{1}{g}=3$$

Express g\times \frac{1}{g} as a single fraction.

$$\frac{g}{g}\times 3=3$$

Cancel out g in both numerator and denominator.

$$1\times 3=3$$

Multiply 1 and 3 to get 3.

$$3=3$$

Compare 3 and 3.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to 0.

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