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 the numerators and denominators

Using the Factoring Trinomials and Multiplying Rational Expressions knowledge points

$$
LATEXBLOCK0
$$

Multiply and simplify the expression

Using the Multiplying Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Identify the missing values

Using the Simplifying Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

Comparing the terms:

• The numerator term \(x - [ ? ]\) corresponds to \(x - 7\), so the green box \([ ? ]\) is \(7\).
• The denominator term \(x + [ \quad ]\) corresponds to \(x + 2\), so the grey box \([ \quad ]\) is \(2\).

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:

$$\frac{(x + 3)(x - \text{7})}{(x + \text{2})(x + 9)}$$