Question

Find the horizontal asymptote of the function

Answer 1

`\cfrac{(x-1)(x-3)^2 (x+1)^2}{(x-2)(x+2)(x-1)(x+3)}\implies \cfrac{(x-3)^2 (x+1)^2}{(x-2)(x+2)(x+3)} \\\\\\ \cfrac{(x-3)^2 (x+1)^2}{(x^2 - 4)(x+3)}\implies \cfrac{(x^2-6x+9)(x^2+2x+1)}{(x^2 - 4)(x+3)} \\\\\\ \cfrac{x^4-4x^3-2x^2+12x+9}{x^3+3x^2-4x-12}\qquad \begin{array}{llll} \textit{the numerator has a higher}\\ \textit{degree than the denominator}\\ \textit{thus \underline{no horizontal asymptote}} \end{array}`