Algebra Examples

$\frac{x^{2} - 2 x - 8}{3 x^{2} + 9 x} \cdot \frac{3 x - 18}{x + 2}$

Step 1

Factor $x^{2} - 2 x - 8$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 2)}{3 x^{2} + 9 x} \cdot \frac{3 x - 18}{x + 2}$

Step 2

Simplify terms.

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Step 2.1

Factor $3 x$ out of $3 x^{2} + 9 x$ .

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Step 2.1.1

Factor $3 x$ out of $3 x^{2}$ .

$\frac{(x - 4) (x + 2)}{3 x (x) + 9 x} \cdot \frac{3 x - 18}{x + 2}$

Step 2.1.2

Factor $3 x$ out of $9 x$ .

$\frac{(x - 4) (x + 2)}{3 x (x) + 3 x (3)} \cdot \frac{3 x - 18}{x + 2}$

Step 2.1.3

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

$\frac{(x - 4) (x + 2)}{3 x (x + 3)} \cdot \frac{3 x - 18}{x + 2}$

Step 2.2

Factor $3$ out of $3 x - 18$ .

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Step 2.2.1

Factor $3$ out of $3 x$ .

$\frac{(x - 4) (x + 2)}{3 x (x + 3)} \cdot \frac{3 (x) - 18}{x + 2}$

Step 2.2.2

Factor $3$ out of $- 18$ .

$\frac{(x - 4) (x + 2)}{3 x (x + 3)} \cdot \frac{3 x + 3 \cdot - 6}{x + 2}$

Step 2.2.3

Factor $3$ out of $3 x + 3 \cdot - 6$ .

$\frac{(x - 4) (x + 2)}{3 x (x + 3)} \cdot \frac{3 (x - 6)}{x + 2}$

Step 2.3

Cancel the common factor of $x + 2$ .

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Step 2.3.1

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

$\frac{(x + 2) (x - 4)}{3 x (x + 3)} \cdot \frac{3 (x - 6)}{x + 2}$

Step 2.3.2

Cancel the common factor.

$\frac{(x + 2) (x - 4)}{3 x (x + 3)} \cdot \frac{3 (x - 6)}{x + 2}$

Step 2.3.3

Rewrite the expression.

$\frac{x - 4}{3 x (x + 3)} \cdot (3 (x - 6))$

Step 2.4

Cancel the common factor of $3$ .

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Step 2.4.1

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

$\frac{x - 4}{3 (x (x + 3))} \cdot (3 (x - 6))$

Step 2.4.2

Cancel the common factor.

$\frac{x - 4}{3 (x (x + 3))} \cdot (3 (x - 6))$

Step 2.4.3

Rewrite the expression.

$\frac{x - 4}{x (x + 3)} \cdot (x - 6)$

Step 2.5

Multiply $\frac{x - 4}{x (x + 3)}$ by $x - 6$ .

$\frac{(x - 4) (x - 6)}{x (x + 3)}$