Simplify x/2-x/3

$\frac{x}{2} - \frac{x}{3}$

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{2} \cdot \frac{3}{3} - \frac{x}{3}$

To write $- \frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} \cdot \frac{3}{3} - \frac{x}{3} \cdot \frac{2}{2}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{3}{3}$ .

$\frac{x \cdot 3}{2 \cdot 3} - \frac{x}{3} \cdot \frac{2}{2}$

Multiply $2$ by $3$ .

$\frac{x \cdot 3}{6} - \frac{x}{3} \cdot \frac{2}{2}$

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{x \cdot 3}{6} - \frac{x \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$\frac{x \cdot 3}{6} - \frac{x \cdot 2}{6}$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - x \cdot 2}{6}$

Simplify the numerator.

Factor $x$ out of $x \cdot 3 - x \cdot 2$ .

Factor $x$ out of $x \cdot 3$ .

$\frac{x (3) - x \cdot 2}{6}$

Factor $x$ out of $- x \cdot 2$ .

$\frac{x (3) + x (- 1 \cdot 2)}{6}$

Factor $x$ out of $x (3) + x (- 1 \cdot 2)$ .

$\frac{x (3 - 1 \cdot 2)}{6}$

Multiply $- 1$ by $2$ .

$\frac{x (3 - 2)}{6}$

Subtract $2$ from $3$ .

$\frac{x \cdot 1}{6}$

Multiply $x$ by $1$ .

$\frac{x}{6}$