Question

multiply.
\\(\frac{3x - 3}{x^2 + x - 6} \cdot \frac{x^2 - x - 2}{x - 1}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor each expression

Factor \(3x - 3\) as \(3(x - 1)\), \(x^{2}+x - 6\) as \((x + 3)(x - 2)\), \(x^{2}-x - 2\) as \((x - 2)(x + 1)\).
So the expression becomes \(\frac{3(x - 1)}{(x + 3)(x - 2)}\cdot\frac{(x - 2)(x + 1)}{x - 1}\).

Step2: Cancel common factors

Cancel out the common factors \((x - 1)\) and \((x - 2)\) from the numerator and the denominator.
After canceling, we have \(\frac{3(x + 1)}{x + 3}\).

Answer:

\(\frac{3(x + 1)}{x + 3}\)