Question

use factoring to find the simplified quotient of these rational expressions.

\\\frac{4x^2 - 81}{3x^2 - 7x - 20} \div \frac{2x^2 + 3x - 54}{x^2 - 8x + 16}\\

\\\frac{(2x + ?)(x - 4)}{(3x + 5)(x + \quad)}\\

Explanation:

Factor all polynomial expressions

$$
LATEXBLOCK0
$$

Rewrite division as multiplication and simplify

$$
LATEXBLOCK1
$$

Identify the missing values in the template

$$ \frac{(2x + [?])(x - 4)}{(3x + 5)(x + [ \quad ])} = \frac{(2x + 9)(x - 4)}{(3x + 5)(x + 6)} $$

The missing value in the numerator is \(9\).

Answer:

Use factoring to find the simplified quotient of these rational expressions.

$$\frac{4x^2 - 81}{3x^2 - 7x - 20} \div \frac{2x^2 + 3x - 54}{x^2 - 8x + 16}$$

$$\frac{(2x + 9)(x - 4)}{(3x + 5)(x + 6)}$$