Simplify 2/x-x/3

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

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $x \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

Reorder the factors of $x \cdot 3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 - x \cdot x}{3 x}$

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

Move $x$ .

$\frac{6 - (x \cdot x)}{3 x}$

Multiply $x$ by $x$ .

$\frac{6 - x^{2}}{3 x}$