Algebra Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $x$ .

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Step 1.1.1

Cancel the common factor.

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

Step 1.1.2

Rewrite the expression.

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

Step 1.2

Cancel the common factor of $x - 2$ .

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Subtract $3 x$ from $3 x$ .

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

Step 3.1.3

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

$x \cdot x - 3 \cdot 3$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

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

Step 3.2.2

Multiply $- 3$ by $3$ .

$x^{2} - 9$