Factor 1/6x+3/4(1/2x-4)

$\frac{1}{6} x + \frac{3}{4} (\frac{1}{2} x - 4)$

Step 1

Factor $\frac{1}{12}$ out of each term.

$\frac{1}{12} (2 x + \frac{9 x}{2} - 36)$

Step 2

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

$\frac{1}{12} \cdot (2 x \cdot \frac{2}{2} + \frac{9 x}{2} - 36)$

Step 3

Combine $2 x$ and $\frac{2}{2}$ .

$\frac{1}{12} \cdot (\frac{2 x \cdot 2}{2} + \frac{9 x}{2} - 36)$

Step 4

Combine the numerators over the common denominator.

$\frac{1}{12} \cdot (\frac{2 x \cdot 2 + 9 x}{2} - 36)$

Step 5

To write $- 36$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{12} \cdot (\frac{2 x \cdot 2 + 9 x}{2} - 36 \cdot \frac{2}{2})$

Step 6

Combine $- 36$ and $\frac{2}{2}$ .

$\frac{1}{12} \cdot (\frac{2 x \cdot 2 + 9 x}{2} + \frac{- 36 \cdot 2}{2})$

Step 7

Combine the numerators over the common denominator.

$\frac{1}{12} \cdot \frac{2 x \cdot 2 + 9 x - 36 \cdot 2}{2}$

Step 8

Rewrite $\frac{2 x \cdot 2 + 9 x - 36 \cdot 2}{2}$ in a factored form.

Multiply $2$ by $2$ .

$\frac{1}{12} \cdot \frac{4 x + 9 x - 36 \cdot 2}{2}$

Multiply $- 36$ by $2$ .

$\frac{1}{12} \cdot \frac{4 x + 9 x - 72}{2}$

Add $4 x$ and $9 x$ .

$\frac{1}{12} \cdot \frac{13 x - 72}{2}$