# How do you evaluate the limit (x^2-x-6)/(x+2) as x approaches oo?

Let's manipulate for the expression to a more convenient form $\frac{{x}^{2} - x - 6}{x + 2} = \frac{\frac{{x}^{2} - x - 6}{x}}{\frac{x + 2}{x}} = \frac{\left({x}^{2} / x - \frac{x}{x} - \frac{6}{x}\right)}{\left(\frac{x}{x} + \frac{2}{x}\right)} = \frac{x - 1 - \frac{6}{x}}{1 + \frac{2}{x}}$
Then ${\lim}_{x \rightarrow \infty} \left(\frac{{x}^{2} - x - 6}{x + 2}\right) = {\lim}_{x \rightarrow \infty} \left(\frac{x - 1 - \frac{6}{x}}{1 + \frac{2}{x}}\right) = \frac{\infty - 1 - 0}{1 + 0} = \infty$