Simplify 5/(2x)+3/x+1/(3x)

$\frac{5}{2 x} + \frac{3}{x} + \frac{1}{3 x}$

Find the common denominator.

Multiply $\frac{5}{2 x}$ by $\frac{3}{3}$ .

$\frac{5}{2 x} \cdot \frac{3}{3} + \frac{3}{x} + \frac{1}{3 x}$

Multiply $\frac{5}{2 x}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 x \cdot 3} + \frac{3}{x} + \frac{1}{3 x}$

Multiply $\frac{3}{x}$ by $\frac{6}{6}$ .

$\frac{5 \cdot 3}{2 x \cdot 3} + \frac{3}{x} \cdot \frac{6}{6} + \frac{1}{3 x}$

Multiply $\frac{3}{x}$ by $\frac{6}{6}$ .

$\frac{5 \cdot 3}{2 x \cdot 3} + \frac{3 \cdot 6}{x \cdot 6} + \frac{1}{3 x}$

Multiply $\frac{1}{3 x}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{2 x \cdot 3} + \frac{3 \cdot 6}{x \cdot 6} + \frac{1}{3 x} \cdot \frac{2}{2}$

Multiply $\frac{1}{3 x}$ by $\frac{2}{2}$ .

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

Reorder the factors of $2 x \cdot 3$ .

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

Multiply $2$ by $3$ .

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

Reorder the factors of $x \cdot 6$ .

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

Reorder the factors of $3 x \cdot 2$ .

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Multiply $5$ by $3$ .

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

Multiply $3$ by $6$ .

$\frac{15 + 18 + 2}{6 x}$

Simplify by adding numbers.

Add $15$ and $18$ .

$\frac{33 + 2}{6 x}$

Add $33$ and $2$ .

$\frac{35}{6 x}$