Question

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

\\\frac{x^2 + 2x - 3}{x^2 - x - 30} \cdot \frac{x^2 + 2x - 48}{x^2 - 4x + 3}\\

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

Explanation:

Factor each quadratic trinomial

Using the Factoring Trinomials knowledge point

$$
LATEXBLOCK0
$$

Multiply and simplify the rational expressions

Using the Multiplying Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Identify the missing values in the template

Comparing the simplified expression to the given template:

$$ \frac{(x + 3)(x + [ ? ])}{(x + [ \quad ])(x - 3)} = \frac{(x + 3)(x + 8)}{(x + 5)(x - 3)} $$

The value in the green box with the question mark \([ ? ]\) is \(8\).
The value in the grey box \([ \quad ]\) is \(5\).

Answer:

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

$$\frac{x^2 + 2x - 3}{x^2 - x - 30} \cdot \frac{x^2 + 2x - 48}{x^2 - 4x + 3}$$

The simplified product is <blank>\(\frac{(x + 3)(x + 8)}{(x + 5)(x - 3)}\)</blank>.