Questions: Multiply. Write the answer in simplified form. (p-3) * (6p / (2p^2 - 3p - 9)) = □

Solution Steps

To solve the given expression, we need to follow these steps:

1. Factorize the denominator \(2p^2 - 3p - 9\).
2. Simplify the fraction by canceling out common factors in the numerator and the denominator.
3. Multiply the simplified fraction by \((p-3)\).

First, we need to factorize the denominator \(2p^2 - 3p - 9\). The factorization is: \[ 2p^2 - 3p - 9 = (2p + 3)(p - 3) \]

Next, we simplify the fraction \(\frac{6p}{2p^2 - 3p - 9}\) by substituting the factorized form of the denominator: \[ \frac{6p}{2p^2 - 3p - 9} = \frac{6p}{(2p + 3)(p - 3)} \]

We then multiply the simplified fraction by \((p - 3)\) and cancel out the common factor \((p - 3)\): \[ (p - 3) \cdot \frac{6p}{(2p + 3)(p - 3)} = \frac{6p}{2p + 3} \]

Final Answer