To simplify the expression \((3y^2 - 6y)/(y^2 - y - 2)\), we can start with factoring both the numerator and the denominator.
Step 1: Factor the numerator
The numerator is \(3y^2 - 6y\). We can factor out a common term:
\[ 3y^2 - 6y = 3y(y - 2) \]
Step 2: Factor the denominator
The denominator is \(y^2 - y - 2\). We need to factor this quadratic. We look for two numbers that multiply to \(-2\) and add to \(-1\). Those numbers are \(-2\) and \(1\). Thus, we can factor:
\[ y^2 - y - 2 = (y - 2)(y + 1) \]
Step 3: Rewrite the original expression
Now, substituting the factored forms back into the expression gives us:
\[ \frac{3y(y - 2)}{(y - 2)(y + 1)} \]
Step 4: Cancel common factors
We can see that \((y - 2)\) is a common factor in both the numerator and the denominator. As long as \(y \neq 2\), we can cancel it out:
\[ \frac{3y \cancel{(y - 2)}}{\cancel{(y - 2)}(y + 1)} = \frac{3y}{y + 1} \]
Final Answer:
The simplified expression is:
\[ \frac{3y}{y + 1}, \quad \text{for } y \neq 2 \]