How do you simplify (2x - 4)/ (x^2 - 3x + 2) times (x^2 - 4x)/4?

Jul 2, 2018

$\frac{x \left(x - 4\right)}{2 \left(x - 1\right)}$

Explanation:

Lets find the common factors of each term as explained below:

$2 x - 4$ = $2 \left(x - 2\right)$

${x}^{2} - 4 x$ = $x \left(x - 4\right)$

${x}^{2} - 3 x + 2$ = ${x}^{2} - 1 x - 2 x + 2$ = $x \left(x - 1\right) - 2 \left(x - 1\right)$ = $\left(x - 2\right) \left(x - 1\right)$

So now we have:

$\frac{2 \left(x - 2\right)}{\left(x - 2\right) \left(x - 1\right)} \times \frac{x \left(x - 4\right)}{4}$

$\frac{2 \cancel{x - 2}}{\cancel{x - 2} \left(x - 1\right)} \times \frac{x \left(x - 4\right)}{4}$

$\frac{x \left(x - 4\right)}{2 \left(x - 1\right)}$