Question

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

\\\frac{x^2 + 8x + 15}{x^2 + 10x + 16} \cdot \frac{x^2 + x - 56}{x^2 + 14x + 45}\\

\\\frac{(x + 3)(x - ?)}{(x + \quad)(x + 9)}\\

Explanation:

Factor all trinomials in the expression

$$
LATEXBLOCK0
$$

Substitute factors and simplify the product

$$
LATEXBLOCK1
$$

Identify the missing values in the template

$$ \frac{(x + 3)(x - [?])}{(x + [ \quad ])(x + 9)} = \frac{(x + 3)(x - 7)}{(x + 2)(x + 9)} $$

$$ [?] = 7, \quad [ \quad ] = 2 $$

Answer:

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

$$\frac{x^2 + 8x + 15}{x^2 + 10x + 16} \cdot \frac{x^2 + x - 56}{x^2 + 14x + 45}$$

The simplified product is <blank>\(\frac{(x + 3)(x - 7)}{(x + 2)(x + 9)}\)</blank>.