Simplify x/3-x/5

$\frac{x}{3} - \frac{x}{5}$

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{3} \cdot \frac{5}{5} - \frac{x}{5}$

To write $- \frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} \cdot \frac{5}{5} - \frac{x}{5} \cdot \frac{3}{3}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{3}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{3 \cdot 5} - \frac{x}{5} \cdot \frac{3}{3}$

Multiply $3$ by $5$ .

$\frac{x \cdot 5}{15} - \frac{x}{5} \cdot \frac{3}{3}$

Multiply $\frac{x}{5}$ by $\frac{3}{3}$ .

$\frac{x \cdot 5}{15} - \frac{x \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{x \cdot 5}{15} - \frac{x \cdot 3}{15}$

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - x \cdot 3}{15}$

Simplify the numerator.

Factor $x$ out of $x \cdot 5 - x \cdot 3$ .

Factor $x$ out of $x \cdot 5$ .

$\frac{x (5) - x \cdot 3}{15}$

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

$\frac{x (5) + x (- 1 \cdot 3)}{15}$

Factor $x$ out of $x (5) + x (- 1 \cdot 3)$ .

$\frac{x (5 - 1 \cdot 3)}{15}$

Multiply $- 1$ by $3$ .

$\frac{x (5 - 3)}{15}$

Subtract $3$ from $5$ .

$\frac{x \cdot 2}{15}$

Move $2$ to the left of $x$ .

$\frac{2 x}{15}$