# How do you simplify 12/(x^2-x) * (x^2-1)/(4x-2)?

Oct 14, 2015

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

#### Explanation:

Your starting expression looks like this

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

The fist fraction can be written as

$\frac{12}{x \left(x - 1\right)}$

The second fraction can be written as

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

The expression can thus be simplified to

$\frac{12}{x \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 1\right)}}}} \cdot \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 1\right)}}} \left(x + 1\right)}{2 \left(2 x - 1\right)} = \textcolor{g r e e n}{\frac{6 \left(x + 1\right)}{x \left(2 x - 1\right)}}$