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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $3$ by $5$ .

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

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

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

Multiply $5$ by $3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Factor $2$ out of $2 \cdot 3 + 2 x (5 x)$ .

Factor $2$ out of $2 \cdot 3$ .

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

Factor $2$ out of $2 x (5 x)$ .

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

Factor $2$ out of $2 (3) + 2 (x (5 x))$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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