Simplify ((x^2-x-12)/(3x-9))÷((x-4)/12)

$\frac{x^{2} - x - 12}{3 x - 9} \div \frac{x - 4}{12}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - x - 12}{3 x - 9} \cdot \frac{12}{x - 4}$

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.

$\frac{(x - 4) (x + 3)}{3 x - 9} \cdot \frac{12}{x - 4}$

Simplify terms.

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

Factor $3$ out of $3 x$ .

$\frac{(x - 4) (x + 3)}{3 (x) - 9} \cdot \frac{12}{x - 4}$

Factor $3$ out of $- 9$ .

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

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

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

Cancel the common factor of $x - 4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

Simplify ((x^2-x-12)/(3x-9))÷((x-4)/12)

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