Simplify 2/(9x)-(2x)/3

$\frac{2}{9 x} - \frac{2 x}{3}$

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

$\frac{2}{9 x} - \frac{2 x}{3} \cdot \frac{3 x}{3 x}$

Write each expression with a common denominator of $9 x$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{2}{9 x} - \frac{2 x (3 x)}{3 (3 x)}$

Multiply $3$ by $3$ .

$\frac{2}{9 x} - \frac{2 x (3 x)}{9 x}$

Combine the numerators over the common denominator.

$\frac{2 - 2 x (3 x)}{9 x}$

Simplify the numerator.

Factor $2$ out of $2 - 2 x (3 x)$ .

Factor $2$ out of $2$ .

$\frac{2 (1) - 2 x (3 x)}{9 x}$

Factor $2$ out of $- 2 x (3 x)$ .

$\frac{2 (1) + 2 (- x (3 x))}{9 x}$

Factor $2$ out of $2 (1) + 2 (- x (3 x))$ .

$\frac{2 (1 - x (3 x))}{9 x}$

Rewrite using the commutative property of multiplication.

$\frac{2 (1 - 1 \cdot 3 x \cdot x)}{9 x}$

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

Move $x$ .

$\frac{2 (1 - 1 \cdot 3 (x \cdot x))}{9 x}$

Multiply $x$ by $x$ .

$\frac{2 (1 - 1 \cdot 3 x^{2})}{9 x}$

Multiply $- 1$ by $3$ .

$\frac{2 (1 - 3 x^{2})}{9 x}$