Oblique asymptote of exponential

Question

How do I derive the oblique asymptote for $$y = \frac{x+2}{e^x - 2}$$

In case it's needed, the supposed answer is $$ y = -0.5x - 1$$

Answer 1

Hint: Just find the slop $$m=\lim_{x\to\pm\infty}\dfrac{y}{x}$$ which gives $m=-\dfrac12$ as $x\to-\infty$ and then find $$h=\lim_{x\to\pm\infty}y-mx=-1$$

Answer 2

Your function has no an oblique asymptote because $$\lim_{x\rightarrow+\infty}\frac{x+2}{e^x-2}=0$$ and $$\lim_{x\rightarrow-\infty}\frac{x+2}{e^x-2}=+\infty$$