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.

Move $3$ to the left of $x$ .

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

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

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

Add $3 x$ and $2 x$ .

$\frac{5 x}{6}$