Question

Multiply. State the product in simplest form. (k²+7k+12)/(k²+10k+21)*(15)/(3k+12),k!=-3,-4,-7 (15)/(3k+21) (5(k+5))/((k+3)(k+4)) (5)/(k+7)

Answer 1

To multiply the given expression and state the product in simplest form, we need to simplify each expression separately and then multiply the simplified forms.

Step-by-step explanation:

To multiply the expression (k²+7k+12)/(k²+10k+21)*(15)/(3k+12) and state the product in simplest form, we need to simplify each expression separately and then multiply the simplified forms. Here are the steps:

1. Factor the numerator and denominator of the first expression, (k²+7k+12)/(k²+10k+21), to get [(k+3)(k+4)]/[(k+7)(k+3)].
2. Cancel out the common factor of (k+3) from the numerator and denominator.
3. Factor the denominator of the second expression, (3k+12), to get 3(k+4).
4. Cancel out the common factor of (k+4) from the numerator and denominator.
5. Multiply the simplified forms: [(k+4)/(k+7)] * (15/3) = (5(k+4))/(k+7).

So, the simplified form of the given expression is (5(k+4))/(k+7).