Question

current objective
divide rational expressions

question

divide and simplify:
\\\frac{3x^2 + 15x + 18}{x^2 + 2x - 24} \div \frac{x + 3}{x - 4}\\

Explanation:

Convert division to multiplication

Using the Dividing Rational Expressions knowledge point

$$ \frac{3x^2 + 15x + 18}{x^2 + 2x - 24} \div \frac{x + 3}{x - 4} = \frac{3x^2 + 15x + 18}{x^2 + 2x - 24} \cdot \frac{x - 4}{x + 3} $$

Factor the first numerator

Using the Greatest Common Factor Factoring and Factoring Trinomials knowledge points

$$
LATEXBLOCK0
$$

Factor the first denominator

Using the Factoring Trinomials knowledge point

$$ x^2 + 2x - 24 = (x + 6)(x - 4) $$

Substitute and simplify

Using the Simplifying Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Answer:

$$\frac{3(x + 2)}{x + 6}$$