Simplify (3x)/(2x-8)+x/(x-4)

$\frac{3 x}{2 x - 8} + \frac{x}{x - 4}$

Step 1

Factor $2$ out of $2 x - 8$ .

Factor $2$ out of $2 x$ .

$\frac{3 x}{2 (x) - 8} + \frac{x}{x - 4}$

Factor $2$ out of $- 8$ .

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

Factor $2$ out of $2 x + 2 \cdot - 4$ .

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

Step 2

To write $\frac{x}{x - 4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Write each expression with a common denominator of $2 (x - 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{x - 4}$ by $\frac{2}{2}$ .

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

Reorder the factors of $(x - 4) \cdot 2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Move $2$ to the left of $x$ .

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

Add $3 x$ and $2 x$ .

$\frac{5 x}{2 (x - 4)}$