Find the Product (2y)/(y-3)*(4y-12)/(2y+6)

$\frac{2 y}{y - 3} \cdot \frac{4 y - 12}{2 y + 6}$

Step 1

Factor $4$ out of $4 y - 12$ .

Factor $4$ out of $4 y$ .

$\frac{2 y}{y - 3} \cdot \frac{4 (y) - 12}{2 y + 6}$

Factor $4$ out of $- 12$ .

$\frac{2 y}{y - 3} \cdot \frac{4 y + 4 \cdot - 3}{2 y + 6}$

Factor $4$ out of $4 y + 4 \cdot - 3$ .

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

Step 2

Factor $2$ out of $2 y + 6$ .

Factor $2$ out of $2 y$ .

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

Factor $2$ out of $6$ .

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

Factor $2$ out of $2 y + 2 \cdot 3$ .

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

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $2 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $y - 3$ .

Factor $y - 3$ out of $4 (y - 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y \cdot \frac{4}{y + 3}$

Step 5

Combine $y$ and $\frac{4}{y + 3}$ .

$\frac{y \cdot 4}{y + 3}$

Step 6

Move $4$ to the left of $y$ .

$\frac{4 y}{y + 3}$