Simplify -1/9x+3/9x

$- \frac{1}{9} x + \frac{3}{9} x$

Step 1

Simplify each term.

Combine $x$ and $\frac{1}{9}$ .

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

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3$ .

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

Cancel the common factors.

Factor $3$ out of $9$ .

$- \frac{x}{9} + \frac{3 \cdot 1}{3 \cdot 3} x$

Cancel the common factor.

$- \frac{x}{9} + \frac{3 \cdot 1}{3 \cdot 3} x$

Rewrite the expression.

$- \frac{x}{9} + \frac{1}{3} x$

Combine $\frac{1}{3}$ and $x$ .

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

Step 2

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

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

Step 3

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

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

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

Multiply $3$ by $3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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

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

Add $- x$ and $3 x$ .

$\frac{2 x}{9}$