Simplify x/(3x-6)+1/8

$\frac{x}{3 x - 6} + \frac{1}{8}$

Step 1

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

$\frac{x}{3 (x) - 6} + \frac{1}{8}$

Factor $3$ out of $- 6$ .

$\frac{x}{3 x + 3 \cdot - 2} + \frac{1}{8}$

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{x}{3 (x - 2)} + \frac{1}{8}$

Step 2

To write $\frac{x}{3 (x - 2)}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{x}{3 (x - 2)} \cdot \frac{8}{8} + \frac{1}{8}$

Step 3

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{3 (x - 2)}{3 (x - 2)}$ .

$\frac{x}{3 (x - 2)} \cdot \frac{8}{8} + \frac{1}{8} \cdot \frac{3 (x - 2)}{3 (x - 2)}$

Step 4

Write each expression with a common denominator of $24 (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{3 (x - 2)}$ by $\frac{8}{8}$ .

$\frac{x \cdot 8}{3 (x - 2) \cdot 8} + \frac{1}{8} \cdot \frac{3 (x - 2)}{3 (x - 2)}$

Multiply $8$ by $3$ .

$\frac{x \cdot 8}{24 (x - 2)} + \frac{1}{8} \cdot \frac{3 (x - 2)}{3 (x - 2)}$

Multiply $\frac{1}{8}$ by $\frac{3 (x - 2)}{3 (x - 2)}$ .

$\frac{x \cdot 8}{24 (x - 2)} + \frac{3 (x - 2)}{8 (3 (x - 2))}$

Multiply $3$ by $8$ .

$\frac{x \cdot 8}{24 (x - 2)} + \frac{3 (x - 2)}{24 (x - 2)}$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot 8 + 3 (x - 2)}{24 (x - 2)}$

Step 6

Simplify the numerator.

Move $8$ to the left of $x$ .

$\frac{8 \cdot x + 3 (x - 2)}{24 (x - 2)}$

Apply the distributive property.

$\frac{8 x + 3 x + 3 \cdot - 2}{24 (x - 2)}$

Multiply $3$ by $- 2$ .

$\frac{8 x + 3 x - 6}{24 (x - 2)}$

Add $8 x$ and $3 x$ .

$\frac{11 x - 6}{24 (x - 2)}$