Algebra Examples

$\frac{x - 2}{x + 3} \cdot \frac{x^{2} - 9}{4 x - 8}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{x - 2}{x + 3} \cdot \frac{x^{2} - 3^{2}}{4 x - 8}$

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 $b = 3$ .

$\frac{x - 2}{x + 3} \cdot \frac{(x + 3) (x - 3)}{4 x - 8}$

Step 2

Simplify terms.

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Step 2.1

Factor $4$ out of $4 x - 8$ .

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Step 2.1.1

Factor $4$ out of $4 x$ .

$\frac{x - 2}{x + 3} \cdot \frac{(x + 3) (x - 3)}{4 (x) - 8}$

Step 2.1.2

Factor $4$ out of $- 8$ .

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

Step 2.1.3

Factor $4$ out of $4 x + 4 \cdot - 2$ .

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

Step 2.2

Cancel the common factor of $x - 2$ .

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Step 2.2.1

Factor $x - 2$ out of $4 (x - 2)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\frac{1}{x + 3} \cdot \frac{(x + 3) (x - 3)}{4}$

Step 2.3

Cancel the common factor of $x + 3$ .

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Step 2.3.1

Cancel the common factor.

$\frac{1}{x + 3} \cdot \frac{(x + 3) (x - 3)}{4}$

Step 2.3.2

Rewrite the expression.

$\frac{x - 3}{4}$