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

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

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 2$ .

Factor $x - 2$ out of $(x + 3) (x - 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$(x - 3) \cdot (x + 3)$

Step 2

Expand $(x - 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$x (x + 3) - 3 (x + 3)$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 3 (x + 3)$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 3 x - 3 \cdot 3$

Step 3

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot 3 - 3 x - 3 \cdot 3$ .

Reorder the factors in the terms $x \cdot 3$ and $- 3 x$ .

$x \cdot x + 3 x - 3 x - 3 \cdot 3$

Subtract $3 x$ from $3 x$ .

$x \cdot x + 0 - 3 \cdot 3$

Add $x \cdot x$ and $0$ .

$x \cdot x - 3 \cdot 3$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} - 3 \cdot 3$

Multiply $- 3$ by $3$ .

$x^{2} - 9$