Simplify x/2+x/5+x/3

$\frac{x}{2} + \frac{x}{5} + \frac{x}{3}$

Step 1

Find the common denominator.

Multiply $\frac{x}{2}$ by $\frac{15}{15}$ .

$\frac{x}{2} \cdot \frac{15}{15} + \frac{x}{5} + \frac{x}{3}$

Multiply $\frac{x}{2}$ by $\frac{15}{15}$ .

$\frac{x \cdot 15}{2 \cdot 15} + \frac{x}{5} + \frac{x}{3}$

Multiply $\frac{x}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 15}{2 \cdot 15} + \frac{x}{5} \cdot \frac{6}{6} + \frac{x}{3}$

Multiply $\frac{x}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 15}{2 \cdot 15} + \frac{x \cdot 6}{5 \cdot 6} + \frac{x}{3}$

Multiply $\frac{x}{3}$ by $\frac{10}{10}$ .

$\frac{x \cdot 15}{2 \cdot 15} + \frac{x \cdot 6}{5 \cdot 6} + \frac{x}{3} \cdot \frac{10}{10}$

Multiply $\frac{x}{3}$ by $\frac{10}{10}$ .

$\frac{x \cdot 15}{2 \cdot 15} + \frac{x \cdot 6}{5 \cdot 6} + \frac{x \cdot 10}{3 \cdot 10}$

Multiply $2$ by $15$ .

$\frac{x \cdot 15}{30} + \frac{x \cdot 6}{5 \cdot 6} + \frac{x \cdot 10}{3 \cdot 10}$

Multiply $5$ by $6$ .

$\frac{x \cdot 15}{30} + \frac{x \cdot 6}{30} + \frac{x \cdot 10}{3 \cdot 10}$

Multiply $3$ by $10$ .

$\frac{x \cdot 15}{30} + \frac{x \cdot 6}{30} + \frac{x \cdot 10}{30}$

Step 2

Combine the numerators over the common denominator.

$\frac{x \cdot 15 + x \cdot 6 + x \cdot 10}{30}$

Step 3

Simplify each term.

Move $15$ to the left of $x$ .

$\frac{15 \cdot x + x \cdot 6 + x \cdot 10}{30}$

Move $6$ to the left of $x$ .

$\frac{15 x + 6 \cdot x + x \cdot 10}{30}$

Move $10$ to the left of $x$ .

$\frac{15 x + 6 x + 10 x}{30}$

Step 4

Simplify by adding terms.

Add $15 x$ and $6 x$ .

$\frac{21 x + 10 x}{30}$

Add $21 x$ and $10 x$ .

$\frac{31 x}{30}$