Question

get familiar with this topic by reviewing instruction and answering a couple of questions.

question

divide:
\\\frac{14x^3 - 56x}{x^2 - x - 20} \div \frac{7x^2 - 21x - 70}{x^2 + 5x - 24}\\

note: enter answer in factored form.

provide your answer below:

Explanation:

Rewrite division as multiplication

Using the Dividing Rational Expressions knowledge point

$$ \frac{14x^3 - 56x}{x^2 - x - 20} \div \frac{7x^2 - 21x - 70}{x^2 + 5x - 24} = \frac{14x^3 - 56x}{x^2 - x - 20} \cdot \frac{x^2 + 5x - 24}{7x^2 - 21x - 70} $$

Factor the first numerator

Using the Greatest Common Factor Factoring and Difference of Squares knowledge points

$$ 14x^3 - 56x = 14x(x^2 - 4) = 14x(x - 2)(x + 2) $$

Factor the remaining polynomials

Using the Factoring Trinomials and Greatest Common Factor Factoring knowledge points

$$
LATEXBLOCK0
$$

Substitute and simplify

Using the Multiplying Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Answer:

Divide:

$$ \frac{14x^3 - 56x}{x^2 - x - 20} \div \frac{7x^2 - 21x - 70}{x^2 + 5x - 24} $$

Provide your answer below:
<blank>\(\frac{2x(x-2)(x-3)(x+8)}{(x-5)^2(x+4)}\)</blank>