# How do you simplify (2x^2-12x)/(x^2-7x+6)div(2x)/(3x-3)?

Oct 17, 2016

The expression simplifies to $3$, with restrictions being $x \ne 6 , 1 \mathmr{and} 0$.

#### Explanation:

Turn into a multiplication and factor.

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

$= \frac{2 x \left(x - 6\right)}{\left(x - 6\right) \left(x - 1\right)} \times \frac{3 \left(x - 1\right)}{2 x}$

$= 3$

Finally, let us note the restrictions on the variable. These are found by setting the denominator to $0$ and solving.

${x}^{2} - 7 x + 6 = 0$

$\left(x - 6\right) \left(x - 1\right) = 0$

$x = 6 \mathmr{and} 1$

AND

$3 x - 3 = 0$

$3 \left(x - 1\right) = 0$

$x = 1$

AND

$2 x = 0$

$x = 0$

Hence. $x \ne 6 , 1 , 0$.

Hopefully this helps!