Find the Product (4k+2)/(k^2-4)*(k-2)/(2k+1)

$\frac{4 k + 2}{k^{2} - 4} \cdot \frac{k - 2}{2 k + 1}$

Factor $2$ out of $4 k + 2$ .

Factor $2$ out of $4 k$ .

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

Factor $2$ out of $2$ .

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

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

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

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = k$ and $b = 2$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2 k + 1$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{(k + 2) (k - 2)} \cdot (k - 2)$

Cancel the common factor of $k - 2$ .

Factor $k - 2$ out of $(k + 2) (k - 2)$ .

$\frac{2}{(k - 2) (k + 2)} \cdot (k - 2)$

Cancel the common factor.

$\frac{2}{(k - 2) (k + 2)} \cdot (k - 2)$

Rewrite the expression.

$\frac{2}{k + 2}$