Simplify ((2x^2-12x)/(x^2-7x+6))÷((2x)/(3x-3))

$\frac{2 x^{2} - 12 x}{x^{2} - 7 x + 6} \div \frac{2 x}{3 x - 3}$

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x^{2} - 12 x}{x^{2} - 7 x + 6} \cdot \frac{3 x - 3}{2 x}$

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

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

$\frac{2 x (x) - 12 x}{x^{2} - 7 x + 6} \cdot \frac{3 x - 3}{2 x}$

Factor $2 x$ out of $- 12 x$ .

$\frac{2 x (x) + 2 x (- 6)}{x^{2} - 7 x + 6} \cdot \frac{3 x - 3}{2 x}$

Factor $2 x$ out of $2 x (x) + 2 x (- 6)$ .

$\frac{2 x (x - 6)}{x^{2} - 7 x + 6} \cdot \frac{3 x - 3}{2 x}$

Factor $x^{2} - 7 x + 6$ 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 $6$ and whose sum is $- 7$ .

$- 6, - 1$

Write the factored form using these integers.

$\frac{2 x (x - 6)}{(x - 6) (x - 1)} \cdot \frac{3 x - 3}{2 x}$

Simplify terms.

Cancel the common factor of $2 x$ .

Cancel the common factor.

$\frac{2 x (x - 6)}{(x - 6) (x - 1)} \cdot \frac{3 x - 3}{2 x}$

Rewrite the expression.

$\frac{x - 6}{(x - 6) (x - 1)} (3 x - 3)$

Cancel the common factor of $x - 6$ .

Cancel the common factor.

$\frac{x - 6}{(x - 6) (x - 1)} (3 x - 3)$

Rewrite the expression.

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

Multiply $\frac{1}{x - 1}$ by $3 x - 3$ .

$\frac{3 x - 3}{x - 1}$

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 3$ .

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

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

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Divide $3$ by $1$ .

$3$

Simplify ((2x^2-12x)/(x^2-7x+6))÷((2x)/(3x-3))

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