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

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

To divide by a fraction, multiply by its reciprocal.

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

Factor $x^{2} - x - 12$ using the AC method.

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 $- 12$ and whose sum is $- 1$ .

$- 4, 3$

Write the factored form using these integers.

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

Simplify terms.

Factor $4$ out of $4 x + 12$ .

Factor $4$ out of $4 x$ .

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

Factor $4$ out of $12$ .

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

Factor $4$ out of $4 x + 4 \cdot 3$ .

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{(x - 4) (x + 3)}{2 (x + 3)}$ by $\frac{3}{x^{2} - 6 x + 8}$ .

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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.

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

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

Cancel the common factor of $x - 4$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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