Question

X^3 + 3x^2 - 4x - 12 / (x - 2)(x + 3)

Answer 1

Відповідь: х+2.

Пояснення:

розв'язання завдання додаю

Answer 2

To simplify the rational expression $\frac{x^3 + 3x^2 - 4x - 12}{(x - 2)(x + 3)}$, you can start by factoring the numerator and denominator and then canceling any common factors:

1. Factor the numerator: $x^3 + 3x^2 - 4x - 12$

   You can first look for a common factor among the terms: $x(x^2 + 3x - 4) - 12$

   Now, factor the quadratic expression $x^2 + 3x - 4$: $(x + 4)(x - 1)$

   So, the numerator is factored as $x(x + 4)(x - 1) - 12$.

2. Factor the denominator: $(x - 2)(x + 3)$

Now, the rational expression becomes:

$\frac{x(x + 4)(x - 1) - 12}{(x - 2)(x + 3)}$

Next, cancel any common factors between the numerator and denominator:

$\frac{x(x + 4)(x - 1) - 12}{(x - 2)(x + 3)} = \frac{x(x + 4)(x - 1 - 12)}{(x - 2)(x + 3)}$

Now, the expression is simplified.