Question

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

\\\frac{x^2 - 4}{x^2 + 7x + 10} \cdot \frac{x^2 + 10x + 9}{x^2 - 81}\\

\\\frac{(x - 2)(x + ?)}{(x + \quad)(x - 9)}\\

Explanation:

Factor the numerators and denominators

Using the Factoring Trinomials and Simplifying Rational Expressions knowledge points

$$
LATEXBLOCK0
$$

Multiply and simplify the rational expressions

Using the Simplifying Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Identify the missing values in the blanks

Comparing the simplified product to the given template:

$$ \frac{(x - 2)(x + [ ? ])}{(x + [ \quad ])(x - 9)} = \frac{(x - 2)(x + 1)}{(x + 5)(x - 9)} $$

The green box with the question mark \([ ? ]\) is \(1\), and the grey box is \(5\).

Answer:

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

$$\frac{x^2 - 4}{x^2 + 7x + 10} \cdot \frac{x^2 + 10x + 9}{x^2 - 81}$$

$$\frac{(x - 2)(x + \text{1})}{(x + \text{5})(x - 9)}$$