Answer
See explanation
Work Step by Step
Let the rational function be $$f(x)=\frac{P(x)}{Q(x)}$$ where $$\text{degree }P=\text{degree }Q+1$$
To determine the slant asymptote we divide $P(x)$ by $(Q(x)$:
$$Px)\div Q(x)=L(x)+\frac{R(x)}{Q(x)}$$, where
* $L(x)$ is the quotient, which will be a linear function $L(x)=mx+n$
* $R(x)$ is the remainder, where $\text{degree }R<\text{degree }Q$
When $x\rightarrow \infty$ or $x\rightarrow -\infty$, we have $\frac{R(x)}{Q(x)}\rightarrow 0$, so $$f(x)\approx L(x)$$
The slant asymptote is $$y=L(x).$$
