Algebra Examples

$\frac{x + 2}{x^{2} - 9} \cdot \frac{x + 3}{x^{2} - 4}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{x + 2}{x^{2} - 3^{2}} \cdot \frac{x + 3}{x^{2} - 4}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{x + 2}{(x + 3) (x - 3)} \cdot \frac{x + 3}{x^{2} - 4}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

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

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x + 2$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $x + 3$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 3.3

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

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