Simplify x/5+2/(3x)

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

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

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

To write $\frac{2}{3 x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

$\frac{x (3 x)}{5 (3 x)} + \frac{2}{3 x} \cdot \frac{5}{5}$

Multiply $3$ by $5$ .

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

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

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

Multiply $5$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $5$ .

$\frac{3 x^{2} + 10}{15 x}$