Simplify ((x-3)(x-2))/((x+2)(x-2))*((x+6)(x+5))/((x+5)(x-3))

$\frac{(x - 3) (x - 2)}{(x + 2) (x - 2)} \cdot \frac{(x + 6) (x + 5)}{(x + 5) (x - 3)}$

Step 1

Cancel the common factor of $x - 3$ .

Factor $x - 3$ out of $(x + 5) (x - 3)$ .

$\frac{(x - 3) (x - 2)}{(x + 2) (x - 2)} \cdot \frac{(x + 6) (x + 5)}{(x - 3) (x + 5)}$

Cancel the common factor.

$\frac{(x - 3) (x - 2)}{(x + 2) (x - 2)} \cdot \frac{(x + 6) (x + 5)}{(x - 3) (x + 5)}$

Rewrite the expression.

$\frac{x - 2}{(x + 2) (x - 2)} \cdot \frac{(x + 6) (x + 5)}{x + 5}$

Step 2

Multiply $\frac{x - 2}{(x + 2) (x - 2)}$ by $\frac{(x + 6) (x + 5)}{x + 5}$ .

$\frac{(x - 2) ((x + 6) (x + 5))}{(x + 2) (x - 2) (x + 5)}$

Step 3

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{(x - 2) ((x + 6) (x + 5))}{(x + 2) (x - 2) (x + 5)}$

Rewrite the expression.

$\frac{(x + 6) (x + 5)}{(x + 2) (x + 5)}$

Step 4

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{(x + 6) (x + 5)}{(x + 2) (x + 5)}$

Rewrite the expression.

$\frac{x + 6}{x + 2}$