The limit of the given expression as $x \to \infty$ does not exist, as the result tends to $-\infty$.

Would you like a detailed step-by-step breakdown of how this result is obtained?

Here are 5 related questions for further practice:

1. What is the limit as $x \to \infty$ for $\frac{x^2 + 4x + 5}{x + 1}$?
2. How do we handle indeterminate forms when calculating limits?
3. What is the horizontal asymptote of $\frac{2x^2 - 5x + 1}{x^2 + 3x + 2}$?
4. Can you compute the limit of $\frac{x^3 - x^2}{x - 1}$ as $x \to \infty$?
5. What is the limit $\lim_{x \to -\infty} \frac{2x^2 - x + 4}{x^2 + x + 1}$?

Tip: When working with limits at infinity, dividing all terms by the highest power of $x$ can help simplify complex expressions.