Simplify ((12x-96)/(x^2-4x-32))/((6x^2-6x-12)/(3x+3))

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{6 x^{2} - 6 x - 12}{3 x + 3}}$

Cancel the common factor of $6 x^{2} - 6 x - 12$ and $3 x + 3$ .

Factor $3$ out of $6 x^{2}$ .

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2}) - 6 x - 12}{3 x + 3}}$

Factor $3$ out of $- 6 x$ .

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2}) + 3 (- 2 x) - 12}{3 x + 3}}$

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

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2} - 2 x) - 12}{3 x + 3}}$

Factor $3$ out of $- 12$ .

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2} - 2 x) + 3 \cdot - 4}{3 x + 3}}$

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

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2} - 2 x - 4)}{3 x + 3}}$

Cancel the common factors.

Factor $3$ out of $3 x$ .

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2} - 2 x - 4)}{3 (x) + 3}}$

Factor $3$ out of $3$ .

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2} - 2 x - 4)}{3 (x) + 3 (1)}}$

Factor $3$ out of $3 (x) + 3 (1)$ .

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2} - 2 x - 4)}{3 (x + 1)}}$

Cancel the common factor.

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{3 (2 x^{2} - 2 x - 4)}{3 (x + 1)}}$

Rewrite the expression.

$\frac{\frac{12 x - 96}{x^{2} - 4 x - 32}}{\frac{2 x^{2} - 2 x - 4}{x + 1}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{12 x - 96}{x^{2} - 4 x - 32} \cdot \frac{x + 1}{2 x^{2} - 2 x - 4}$

Factor $12$ out of $12 x - 96$ .

Factor $12$ out of $12 x$ .

$\frac{12 (x) - 96}{x^{2} - 4 x - 32} \cdot \frac{x + 1}{2 x^{2} - 2 x - 4}$

Factor $12$ out of $- 96$ .

$\frac{12 x + 12 \cdot - 8}{x^{2} - 4 x - 32} \cdot \frac{x + 1}{2 x^{2} - 2 x - 4}$

Factor $12$ out of $12 x + 12 \cdot - 8$ .

$\frac{12 (x - 8)}{x^{2} - 4 x - 32} \cdot \frac{x + 1}{2 x^{2} - 2 x - 4}$

Factor $x^{2} - 4 x - 32$ 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 $- 32$ and whose sum is $- 4$ .

$- 8, 4$

Write the factored form using these integers.

$\frac{12 (x - 8)}{(x - 8) (x + 4)} \cdot \frac{x + 1}{2 x^{2} - 2 x - 4}$

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{12 (x - 8)}{(x - 8) (x + 4)} \cdot \frac{x + 1}{2 x^{2} - 2 x - 4}$

Rewrite the expression.

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

Simplify the denominator.

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

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

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

Factor $2$ out of $- 2 x$ .

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

Factor $2$ out of $- 4$ .

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

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

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

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

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

Factor $x^{2} - x - 2$ 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 $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Write the factored form using these integers.

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

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

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$\frac{2 (6)}{x + 4} \cdot \frac{x + 1}{2 (x - 2) (x + 1)}$

Factor $2$ out of $2 (x - 2) (x + 1)$ .

$\frac{2 (6)}{x + 4} \cdot \frac{x + 1}{2 ((x - 2) (x + 1))}$

Cancel the common factor.

$\frac{2 \cdot 6}{x + 4} \cdot \frac{x + 1}{2 ((x - 2) (x + 1))}$

Rewrite the expression.

$\frac{6}{x + 4} \cdot \frac{x + 1}{(x - 2) (x + 1)}$

Multiply $\frac{6}{x + 4}$ by $\frac{x + 1}{(x - 2) (x + 1)}$ .

$\frac{6 (x + 1)}{(x + 4) ((x - 2) (x + 1))}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{6 (x + 1)}{(x + 4) ((x - 2) (x + 1))}$

Rewrite the expression.

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

Simplify ((12x-96)/(x^2-4x-32))/((6x^2-6x-12)/(3x+3))

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