Simplify ((r-3)(r+9))/((r+2)(r+9))*(2(r+2))/(r-3)

$\frac{(r - 3) (r + 9)}{(r + 2) (r + 9)} \cdot \frac{2 (r + 2)}{r - 3}$

Step 1

Cancel the common factor of $r - 3$ .

Cancel the common factor.

$\frac{(r - 3) (r + 9)}{(r + 2) (r + 9)} \cdot \frac{2 (r + 2)}{r - 3}$

Rewrite the expression.

$\frac{r + 9}{(r + 2) (r + 9)} \cdot (2 (r + 2))$

Step 2

Cancel the common factor of $r + 2$ .

Factor $r + 2$ out of $2 (r + 2)$ .

$\frac{r + 9}{(r + 2) (r + 9)} \cdot ((r + 2) \cdot 2)$

Cancel the common factor.

$\frac{r + 9}{(r + 2) (r + 9)} \cdot ((r + 2) \cdot 2)$

Rewrite the expression.

$\frac{r + 9}{r + 9} \cdot 2$

Step 3

Combine $\frac{r + 9}{r + 9}$ and $2$ .

$\frac{(r + 9) \cdot 2}{r + 9}$

Step 4

Cancel the common factor of $r + 9$ .

Cancel the common factor.

$\frac{(r + 9) \cdot 2}{r + 9}$

Divide $2$ by $1$ .

$2$