# Consider the rational functions: r(x)=(2x−1)/((x^2)−x−2) , s(x)=((x^3)+27)/((x^2)+4) , t(x)=((x^3)−9x)/(x+2)

Consider the following rational functions: $r\left(x\right)=\frac{2x-1}{\left({x}^{2}\right)-x-2}$
$s\left(x\right)=\frac{\left({x}^{3}\right)+27}{\left({x}^{2}\right)+4}$
$t\left(x\right)=\frac{\left({x}^{3}\right)-9x}{x+2}$
$u\left(x\right)=\frac{\left({x}^{2}\right)+x-6}{\left({x}^{2}\right)-25}$
$w\left(x\right)=\frac{\left({x}^{3}\right)+\left(6{x}^{2}\right)+9x}{x+3}$
Which of these rational functions has a horizontal asymptote?

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Ezra Herbert
$r\left(x\right)=\frac{2x-1}{\left({x}^{2}\right)-x-2}=\frac{2x-1}{\left(x-2\right)\left(x+1\right)}$
$s\left(x\right)=\frac{\left({x}^{3}\right)+27}{\left({x}^{2}\right)+4}=\frac{\left(x+3\right)\left(x+9+3x\right)}{\left({x}^{2}\right)+4}$
$t\left(x\right)=\frac{\left({x}^{3}\right)-9x}{x+2}=\frac{x\left(x-3\right)\left(x+3\right)}{x+2}$
$u\left(x\right)=\frac{\left({x}^{2}\right)+x-6}{\left({x}^{2}\right)-25}=\frac{\left(x-2\right)\left(x+3\right)}{\left(x-5\right)\left(x+5\right)}$
$w\left(x\right)=\frac{\left({x}^{3}\right)+\left(6{x}^{2}\right)+9x}{x+3}=x\left(x+3\right)$
r,t and u have horizontal asymptotes