Simplify ((x-3)(2x+1))/((2x+1)(2x+5))*((2x+5)(3x-2))/((x-3)(3x-2))

$\frac{(x - 3) (2 x + 1)}{(2 x + 1) (2 x + 5)} \cdot \frac{(2 x + 5) (3 x - 2)}{(x - 3) (3 x - 2)}$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{(x - 3) (2 x + 1)}{(2 x + 1) (2 x + 5)} \cdot \frac{(2 x + 5) (3 x - 2)}{(x - 3) (3 x - 2)}$

Rewrite the expression.

$\frac{2 x + 1}{(2 x + 1) (2 x + 5)} \cdot \frac{(2 x + 5) (3 x - 2)}{3 x - 2}$

Cancel the common factor of $2 x + 5$ .

Factor $2 x + 5$ out of $(2 x + 1) (2 x + 5)$ .

$\frac{2 x + 1}{(2 x + 5) (2 x + 1)} \cdot \frac{(2 x + 5) (3 x - 2)}{3 x - 2}$

Cancel the common factor.

$\frac{2 x + 1}{(2 x + 5) (2 x + 1)} \cdot \frac{(2 x + 5) (3 x - 2)}{3 x - 2}$

Rewrite the expression.

$\frac{2 x + 1}{2 x + 1} \cdot \frac{3 x - 2}{3 x - 2}$

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

$\frac{(2 x + 1) (3 x - 2)}{(2 x + 1) (3 x - 2)}$

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

Cancel the common factor.

$\frac{(2 x + 1) (3 x - 2)}{(2 x + 1) (3 x - 2)}$

Rewrite the expression.

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

Cancel the common factor of $3 x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$1$