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 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

Using the Multiplying Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

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:

$$\frac{(x + 3)(x + \text{8})}{(x + \text{5})(x - 3)}$$