Simplify ((2n)/(6n+4))((3n+2)/(3n-2))

$(\frac{2 n}{6 n + 4}) (\frac{3 n + 2}{3 n - 2})$

Step 1

Factor $2$ out of $6 n + 4$ .

Factor $2$ out of $6 n$ .

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

Factor $2$ out of $4$ .

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

Factor $2$ out of $2 (3 n) + 2 (2)$ .

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

Step 2

Cancel the common factor of $3 n + 2$ .

Factor $3 n + 2$ out of $2 (3 n + 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 n}{2} \cdot \frac{1}{3 n - 2}$

Step 3

Multiply $\frac{2 n}{2}$ by $\frac{1}{3 n - 2}$ .

$\frac{2 n}{2 (3 n - 2)}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2 (3 n - 2)}$

Rewrite the expression.

$\frac{n}{3 n - 2}$