Simplify (x^2+4x)/(x^2-6x+8)*(x^2-x-2)/(3x^3+12x^2)

$\frac{x^{2} + 4 x}{x^{2} - 6 x + 8} \cdot \frac{x^{2} - x - 2}{3 x^{3} + 12 x^{2}}$

Factor $x$ out of $x^{2} + 4 x$ .

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

$\frac{x \cdot x + 4 x}{x^{2} - 6 x + 8} \cdot \frac{x^{2} - x - 2}{3 x^{3} + 12 x^{2}}$

Factor $x$ out of $4 x$ .

$\frac{x \cdot x + x \cdot 4}{x^{2} - 6 x + 8} \cdot \frac{x^{2} - x - 2}{3 x^{3} + 12 x^{2}}$

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

$\frac{x (x + 4)}{x^{2} - 6 x + 8} \cdot \frac{x^{2} - x - 2}{3 x^{3} + 12 x^{2}}$

Factor $x^{2} - 6 x + 8$ using the AC method.

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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 $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$\frac{x (x + 4)}{(x - 4) (x - 2)} \cdot \frac{x^{2} - x - 2}{3 x^{3} + 12 x^{2}}$

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

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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 $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Write the factored form using these integers.

$\frac{x (x + 4)}{(x - 4) (x - 2)} \cdot \frac{(x - 2) (x + 1)}{3 x^{3} + 12 x^{2}}$

Simplify terms.

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Factor $3 x^{2}$ out of $3 x^{3} + 12 x^{2}$ .

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

$\frac{x (x + 4)}{(x - 4) (x - 2)} \cdot \frac{(x - 2) (x + 1)}{3 x^{2} (x) + 12 x^{2}}$

Factor $3 x^{2}$ out of $12 x^{2}$ .

$\frac{x (x + 4)}{(x - 4) (x - 2)} \cdot \frac{(x - 2) (x + 1)}{3 x^{2} (x) + 3 x^{2} (4)}$

Factor $3 x^{2}$ out of $3 x^{2} (x) + 3 x^{2} (4)$ .

$\frac{x (x + 4)}{(x - 4) (x - 2)} \cdot \frac{(x - 2) (x + 1)}{3 x^{2} (x + 4)}$

Cancel the common factor of $x (x + 4)$ .

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Factor $x (x + 4)$ out of $3 x^{2} (x + 4)$ .

$\frac{x (x + 4)}{(x - 4) (x - 2)} \cdot \frac{(x - 2) (x + 1)}{x (x + 4) (3 x)}$

Cancel the common factor.

$\frac{x (x + 4)}{(x - 4) (x - 2)} \cdot \frac{(x - 2) (x + 1)}{x (x + 4) (3 x)}$

Rewrite the expression.

$\frac{1}{(x - 4) (x - 2)} \cdot \frac{(x - 2) (x + 1)}{3 x}$

Cancel the common factor of $x - 2$ .

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

$\frac{1}{(x - 2) (x - 4)} \cdot \frac{(x - 2) (x + 1)}{3 x}$

Cancel the common factor.

$\frac{1}{(x - 2) (x - 4)} \cdot \frac{(x - 2) (x + 1)}{3 x}$

Rewrite the expression.

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

Multiply $\frac{1}{x - 4}$ and $\frac{x + 1}{3 x}$ .

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

Simplify the expression.

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Move $3$ to the left of $x - 4$ .

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

Reorder factors in $\frac{x + 1}{3 (x - 4) x}$ .

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

Simplify (x^2+4x)/(x^2-6x+8)*(x^2-x-2)/(3x^3+12x^2)

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