Pre-Algebra Examples

$- \frac{3 x}{11} - \frac{11 x}{3}$

Step 1

To write $- \frac{3 x}{11}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{3 x}{11} \cdot \frac{3}{3} - \frac{11 x}{3}$

Step 2

To write $- \frac{11 x}{3}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$- \frac{3 x}{11} \cdot \frac{3}{3} - \frac{11 x}{3} \cdot \frac{11}{11}$

Step 3

Write each expression with a common denominator of $33$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{3 x}{11}$ by $\frac{3}{3}$ .

$- \frac{3 x \cdot 3}{11 \cdot 3} - \frac{11 x}{3} \cdot \frac{11}{11}$

Step 3.2

Multiply $11$ by $3$ .

$- \frac{3 x \cdot 3}{33} - \frac{11 x}{3} \cdot \frac{11}{11}$

Step 3.3

Multiply $\frac{11 x}{3}$ by $\frac{11}{11}$ .

$- \frac{3 x \cdot 3}{33} - \frac{11 x \cdot 11}{3 \cdot 11}$

Step 3.4

Multiply $3$ by $11$ .

$- \frac{3 x \cdot 3}{33} - \frac{11 x \cdot 11}{33}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 3 - 11 x \cdot 11}{33}$

Step 5

Rewrite $\frac{- 3 x \cdot 3 - 11 x \cdot 11}{33}$ in a factored form.

Tap for more steps...

Step 5.1

Factor $- x$ out of $- 3 x \cdot 3 - 11 x \cdot 11$ .

Tap for more steps...

Step 5.1.1

Reorder the expression.

Tap for more steps...

Step 5.1.1.1

Move $x$ .

$\frac{- 3 \cdot 3 x - 11 x \cdot 11}{33}$

Step 5.1.1.2

Move $x$ .

$\frac{- 3 \cdot 3 x - 11 \cdot 11 x}{33}$

Step 5.1.2

Factor $- x$ out of $- 3 \cdot 3 x$ .

$\frac{- x (3 \cdot 3) - 11 \cdot 11 x}{33}$

Step 5.1.3

Factor $- x$ out of $- 11 \cdot 11 x$ .

$\frac{- x (3 \cdot 3) - x (11 \cdot 11)}{33}$

Step 5.1.4

Factor $- x$ out of $- x (3 \cdot 3) - x (11 \cdot 11)$ .

$\frac{- x (3 \cdot 3 + 11 \cdot 11)}{33}$

Step 5.2

Combine exponents.

Tap for more steps...

Step 5.2.1

Multiply $3$ by $3$ .

$\frac{- x (9 + 11 \cdot 11)}{33}$

Step 5.2.2

Multiply $11$ by $11$ .

$\frac{- x (9 + 121)}{33}$

Step 6

Add $9$ and $121$ .

$\frac{- x \cdot 130}{33}$

Step 7

Multiply $130$ by $- 1$ .

$\frac{- 130 x}{33}$