Question

current objective
multiply and divide more than two rational expressions

question

simplify the rational expression: \\(\frac{3q^2 - 12q}{3q - 3} \cdot \frac{q^2 + q - 2}{q^2 + q - 6} \div \frac{3q^2 + 3q}{3q - 6}\\)

provide your answer below:

Explanation:

Convert division to multiplication

Using the Dividing Rational Expressions knowledge point

$$ \frac{3q^2 - 12q}{3q - 3} \cdot \frac{q^2 + q - 2}{q^2 + q - 6} \div \frac{3q^2 + 3q}{3q - 6} = \frac{3q^2 - 12q}{3q - 3} \cdot \frac{q^2 + q - 2}{q^2 + q - 6} \cdot \frac{3q - 6}{3q^2 + 3q} $$

Factor all numerators and denominators

Using the Greatest Common Factor Factoring and Factoring Trinomials knowledge points

$$
LATEXBLOCK0
$$

Substitute factored forms into the expression

Using the Multiplying Rational Expressions knowledge point

$$ \frac{3q(q - 4)}{3(q - 1)} \cdot \frac{(q + 2)(q - 1)}{(q + 3)(q - 2)} \cdot \frac{3(q - 2)}{3q(q + 1)} $$

Combine and simplify the expression

Using the Multiplying Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Answer:

Simplify the rational expression: \(\frac{3q^2 - 12q}{3q - 3} \cdot \frac{q^2 + q - 2}{q^2 + q - 6} \div \frac{3q^2 + 3q}{3q - 6}\) is <blank>\(\frac{(q - 4)(q + 2)}{(q + 3)(q + 1)}\)</blank>.