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

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

Step 1

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2

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

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

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

Move $3$ to the left of $x$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Add $3$ and $1$ .

$\frac{4}{3 x} + \frac{2}{3}$

Step 5

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

$\frac{4}{3 x} + \frac{2}{3} \cdot \frac{x}{x}$

Step 6

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

$\frac{4}{3 x} + \frac{2 x}{3 x}$

Step 7

Combine the numerators over the common denominator.

$\frac{4 + 2 x}{3 x}$

Step 8

Factor $2$ out of $4 + 2 x$ .

Factor $2$ out of $4$ .

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

Factor $2$ out of $2 \cdot 2 + 2 x$ .

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