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

Mar 15, 2018

See a solution process below:

#### Explanation:

We can factor the numerator and denominator as;

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

We can now cancel common term in the numerator and denominator:

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

$\frac{x - 2}{2 x}$

However, we cannot divide by $0$ so we must exclude:

$2 x = 0 \implies x = 0$ and $x - 1 = 0 \implies x 1$

$\frac{{x}^{2} - 3 x + 2}{2 {x}^{2} - 2 x} = \frac{x - 2}{2 x}$ Where: $x \ne 0$ and $x \ne 1$

Or

$\frac{{x}^{2} - 3 x + 2}{2 {x}^{2} - 2 x} = \frac{x}{2 x} - \frac{2}{2 x} = \frac{1}{2} - \frac{1}{x}$ Where: $x \ne 0$ and $x \ne 1$