Question

multiply.
\\(\frac{x - 1}{x^2 - 5x + 6} \cdot \frac{x^2 - x - 2}{4x - 4}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor all polynomials

$\frac{x-1}{(x-2)(x-3)} \cdot \frac{(x-2)(x+1)}{4(x-1)}$

Step2: Cancel common factors

Cancel $x-1$ and $x-2$ from numerator/denominator:
$\frac{1}{x-3} \cdot \frac{x+1}{4}$

Step3: Multiply remaining terms

$\frac{(x+1)}{4(x-3)}$

Answer:

$\frac{x+1}{4(x-3)}$ (or $\frac{x+1}{4x-12}$ when expanded)