Question

current objective
multiply rational expressions

question
multiply: \\(\frac{q^2 + 5q + 6}{6q + 18} \cdot \frac{9q + 27}{q^2 + 8q + 15}\\)

note: enter answer in factored form

provide your answer below:

Explanation:

Factor the numerators

Using the Factoring Trinomials and Greatest Common Factor Factoring knowledge points

$$
LATEXBLOCK0
$$

Factor the denominators

Using the Factoring Trinomials and Greatest Common Factor Factoring knowledge points

$$
LATEXBLOCK1
$$

Multiply the rational expressions

Using the Multiplying Rational Expressions knowledge point

$$ \frac{q^2 + 5q + 6}{6q + 18} \cdot \frac{9q + 27}{q^2 + 8q + 15} = \frac{(q + 2)(q + 3)}{6(q + 3)} \cdot \frac{9(q + 3)}{(q + 3)(q + 5)} $$

Simplify the combined expression

Using the Multiplying Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

Answer:

Multiply: \(\frac{q^2 + 5q + 6}{6q + 18} \cdot \frac{9q + 27}{q^2 + 8q + 15}\)

Provide your answer below:
<blank>\(\frac{3(q+2)}{2(q+5)}\)</blank>