Simplify (x-2)/((x+2)^2)*(x+2)/(2x-4)

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

Step 1

Factor $2$ out of $2 x - 4$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 4$ .

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

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

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

Step 2

Cancel the common factor of $x - 2$ .

Factor $x - 2$ out of $2 (x - 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of ${(x + 2)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + 2} \cdot \frac{1}{2}$

Step 4

Multiply $\frac{1}{x + 2}$ by $\frac{1}{2}$ .

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

Step 5

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

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