Question

Can someone explain to me step by step how to solve this?

I need to find the slant asymptote for f(x)=x^2+1/x-1

Answer 1

`\bf f(x)=\cfrac{x^{\cfrac{}{}\boxed{2}}+1}{x^{\cfrac{}{}\boxed{1}}-1} \\\\ \textit{thus, the oblique asymptote is at }x^2+1 / x-1 \\\\ \begin{array}{llllllll} &&x+1\\ &&--------\\ x-1&|&\quad x^2+0x+1\\ &&-(x^2-x)\\ &&\qquad \quad x+1\\ &&\qquad -(x-1)\\ &&\qquad \qquad \quad 2 \end{array}\\\\ -----------------------\\\\ \textit{so, we have a quotient of x+1, and a remainder of 2}\\ \textit{our slant asymptote is }x+1`