（视频）

The 视频domain of the rational function ( f(x) = \frac{x^3 + 5x^2 - 4}{x^2 + 3x + 2} ) consists of all real numbers except those that make the denominator zero.

The denominator factors as ( x^2 + 3x + 2 = (x + 1)(x + 2) ). Setting each factor equal to zero gives ( x = -1 ) and ( x = -2 ). Therefore, the function is undefined at ( x = -1 ) and ( x = -2 ).

Thus, the domain is all real numbers except ( x = -2 ) and ( x = -1 ), which can be written in interval notation as:

[

(-\infty, -2) \cup (-2, -1) \cup (-1, \infty)

]

or in set notation as:

[

{ x \in \mathbb{R} \mid x \neq -2,\ x \neq -1 }

]