Question

# Consider the following 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) u(x)=((x^2)+x−6)/(x^2−25) w(x)=((x^3)+(6x^2)+9x))/(x+3) Which of these functions has no vertical asymptote?

Rational functions
Consider the following rational functions: $$\displaystyle{r}{\left({x}\right)}=\frac{{{2}{x}−{1}}}{{{x}^{{2}}}}−{x}−{2}{s}{\left({x}\right)}=\frac{{{x}^{{3}}+{27}}}{{{x}^{{2}}+{4}}}$$
$$\displaystyle{t}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}−{9}{x}}}{{{x}+{2}}}$$
$$\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}−{6}}}{{{x}^{{2}}−{25}}}$$
$$\displaystyle{w}{\left({x}\right)}={\left({\left({x}^{{3}}\right)}+{\left({6}{x}^{{2}}\right)}+{9}{x}\right)}\frac{{)}}{{{x}+{3}}}$$
Which of these functions has no vertical asymptote?

$$r(x)=(2x−1)/((x^2)−x−2 )= (2x-1)/(x-2)(x+1)$$
$$s(x)=(x^3+27)/(x^2+4)=(x+3)((x^2)+9+3x)/((x^2)+4)$$
$$t(x)=((x^3)−9x)/(x+2)=(x(x-3)(x+3))/(x+2)$$
$$u(x)=((x^2)+x−6)/(x^2−25)=((x-2)(x+3))/((x-5)(x+5))$$
$$w(x)=((x^3)+(6x^2)+9x))/(x+3)=x(x+3)$$