Questions: Find the product. Simplify your answer. (2s+2)/(s+1) * (3s+3)/(s-8)

Solution Steps

To find the product of the given fractions and simplify the answer, follow these steps:

1. Factorize the numerators and denominators of both fractions.
2. Multiply the numerators together and the denominators together.
3. Simplify the resulting fraction by canceling out any common factors.

First, we factorize the numerators and denominators of both fractions: \[ \frac{2s + 2}{s + 1} \cdot \frac{3s + 3}{s - 8} \] Notice that: \[ 2s + 2 = 2(s + 1) \quad \text{and} \quad 3s + 3 = 3(s + 1) \] So, the fractions become: \[ \frac{2(s + 1)}{s + 1} \cdot \frac{3(s + 1)}{s - 8} \]

Next, we multiply the numerators together and the denominators together: \[ \frac{2(s + 1) \cdot 3(s + 1)}{(s + 1) \cdot (s - 8)} \] This simplifies to: \[ \frac{6(s + 1)^2}{(s + 1)(s - 8)} \]

We can cancel out the common factor \((s + 1)\) in the numerator and the denominator: \[ \frac{6(s + 1)}{s - 8} \]

Final Answer