Question

first up, lets review the assignments learning objectives
get familiar with this topic by reviewing instruction and answering a couple of questions.

question
simplify the rational expression: \\(\frac{3c + 6}{3c + 9} \div \frac{c^2 - 6c + 8}{c^2 + 2c - 3} \cdot \frac{3c - 6}{3c + 12}\\).

provide your answer below:

Explanation:

Factor all numerators and denominators

Using the Greatest Common Factor Factoring and Factoring Trinomials knowledge points

$$
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$$

Rewrite division as multiplication

Using the Dividing Rational Expressions knowledge point

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

Multiply the rational expressions

Using the Multiplying Rational Expressions knowledge point

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

Simplify by canceling common factors

Using the Simplifying Rational Expressions knowledge point

$$
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$$

Answer:

$$\frac{(c + 2)(c - 1)}{(c - 4)(c + 4)}$$