Question

select the correct answer from each drop-down menu.

consider this quotient.

\\\frac{3x^2 - 27x}{2x^2 + 13x - 7} \div \frac{3x}{4x^2 - 1}\\

the simplest form of this quotient has a numerator of choose an answer and a denominator of choose an answer.
the expression does not exist when \\(x =\\) choose an answer.

Explanation:

Factor the numerators and denominators

$$
LATEXBLOCK0
$$

Simplify the quotient

$$
LATEXBLOCK1
$$

Determine excluded values

The expression does not exist when any denominator in the original expression or during the division process is zero:

$$
LATEXBLOCK2
$$

Thus, the excluded values are \(x = -7, -\frac{1}{2}, 0, \frac{1}{2}\).

Answer:

Select the correct answer from each drop-down menu.

Consider this quotient.

$$\frac{3x^2 - 27x}{2x^2 + 13x - 7} \div \frac{3x}{4x^2 - 1}$$

The simplest form of this quotient has a numerator of <blank>\((2x + 1)(x - 9)\)</blank> and a denominator of <blank>\(x + 7\)</blank>.
The expression does not exist when \(x =\) <blank>\(-7, -\frac{1}{2}, 0, \frac{1}{2}\)</blank>.