\( \cdot \lim _ { | x | \rightarrow + \infty } \frac { | x | - 3 x } { | x + 5 | } \)

To evaluate the limit \( \lim _ { | x | \rightarrow + \infty } \frac { | x | - 3 x } { | x + 5 | } \), we need to analyze the behavior of the expression as \( |x| \) approaches infinity. First, as \( |x| \rightarrow +\infty \), we focus on the case where \( x \) is positive, which means \( |x| = x \) and \( |x + 5| = x + 5 \). Thus, the limit transforms to: \[ \lim _ { x \rightarrow + \infty } \frac { x - 3 x } { x + 5 } = \lim _ { x \rightarrow + \infty } \frac { -2x } { x + 5 } \] Now, we can simplify this expression: \[ \frac { -2x } { x + 5 } = \frac { -2 } { 1 + \frac{5}{x} } \] As \( x \) approaches infinity, \( \frac{5}{x} \) approaches 0. Thus, the limit becomes: \[ \lim _ { x \rightarrow + \infty } \frac { -2 } { 1 + 0 } = -2 \] Therefore, the final answer is: \[ \boxed{-2} \]