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

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Add $x$ and $x$ .

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

Step 3

Cancel the common factor of $2 x + 2$ and $2 x - 8$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (x) + 2 (1)$ .

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

Cancel the common factors.

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 8$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 1}{x - 4}$